¶1We address again the prosecution of Craig W. Conkey for the murder in December, 1994, of a woman in Lexington. In 1996, the defendant was convicted of murder in the first degree on theories of deliberate premeditation, extreme atrocity or cruelty, and felony-murder. The jury also found him guilty of armed burglary, armed assault in a dwelling, and armed robbery.
¶2We set forth the facts surrounding the death of the victim. At some point during the night of December 3-4, 1994, the forty-nine year old victim was killed in her home at 915 Massachusetts Avenue in Lexington. Her nearly naked body was found by the police on her bedroom floor on December 6. She was clothed only in a pajama top, which had been ripped open, exposing her breasts. Two buttons were missing from the pajama top, only one of which was found on the bed.
¶3The defendant lived on Massachusetts Avenue, a few doors away, within walking distance. He did not own a car. He was an admitted burglar who “liked” the challenge of breaking into homes when they were occupied. When the police identified his fingerprint and palm print on the victim’s bedroom door, their *63attention focused on him and they reinterviewed him.
¶4The defense was that another person, i.e, the victim’s landlord, who had access to the victim’s home, opportunity, and a motive to harm her, committed the crime.
¶5When interviewed by the police on December 6 (after the body had been discovered), the landlord informed them that he had been in the victim’s home on November 29 to perform requested repairs. The victim had left him a note on November 28 (which he gave to the police)
¶6In response to questions about his actions on the weekend of the murder, the landlord replied that he had a “real problem with dates and times,”
¶7Other evidence concerning the landlord was that he told his fiancée that he believed the victim was strangled “with a pair of stockings and probably raped” and that the back door window had been broken to “make it look[] like a break-in.” The landlord’s fiancée, testifying as a defense witness, recounted that she fell asleep on December 3 at the start of “Saturday Night Live” and did not see the landlord again until about 10 a.m. Sunday morning. She considered herself a “very heavy sleeper,” and stated that the landlord was “an insomniac” who “often got up at night” to work or “go out and drive around.” During the week following the murder, the landlord told his fiancée that he was “upset” she had told the police about his insomnia and night wanderings because they “made him sound . . . guilty” and he expressed “concern[]” that “his fingerprints had been found in the house and that he had keys to the house.” He told another person, a former colleague, that the police had “probably found [his] fingerprints” on the victim’s dresser and that, when he was in her room to do the repair work, he had picked up the telephone on the night table and slipped and knocked it over.
¶8We first discuss the reason for our reversal of the defendant’s convictions and then other issues that may be relevant to a retrial. Further details of the evidence are recounted as necessary.
¶9*661. Prior sexual acts of the third-party culprit. Although the above evidence concerning the landlord was admitted at trial, the defendant claims that other evidence about him should have been admitted as well. He argues that the judge improperly excluded evidence of several instances of the landlord’s sexual aggression toward women (including evidence of a rape allegation against the landlord made seven years before the murder in this case) and evidence that women’s lingerie and sexually explicit photographs of former girl friends had been discovered in the landlord’s home.
¶10A defendant has a constitutional right to present evidence that another may have committed the crime. Commonwealth v. Tague, 434 Mass. 510, 515-516 (2001), cert. denied, 534 U.S. 1146 (2002), citing Commonwealth v. Jewett, 392 Mass. 558, 562 (1984). “A defendant may introduce evidence that tends to show that another person committed the crime or had the motive, intent, and opportunity to commit it.” Commonwealth v. Lawrence, 404 Mass. 378, 387 (1989), quoting Commonwealth v. Harris, 395 Mass. 296, 300 (1985). See Commonwealth v. Murphy, 282 Mass. 593, 597-598 (1933). Normal relevancy considerations apply in determining the admissibility of evidence that someone else committed the crime. Commonwealth v. Jewett, supra. But the defendant must show that “the acts of the other person are so closely connected in point of time and method of operation as to cast doubt upon the identification of [the] defendant as the person who committed the crime.” Commonwealth v. Hunter, 426 Mass. 715, 716-717 (1998), quoting Commonwealth v. Keizer, 377 Mass. 264, 267 (1979). If the evidence is “of substantial probative value, and will not tend to prejudice or confuse, all doubt should be resolved in favor of admissibility.” Commonwealth v. Keizer, supra, quoting Holt v. United States, 342 F.2d 163, 166 (5th Cir. 1965). Because the issue is one of constitutional dimension, we are not bound by an abuse of discretion standard, but rather *67examine the issue independently.
¶11The defendant sought to present the following evidence to establish the landlord’s pattern of sexual aggression toward women who resisted him. That alleged pattern was offered to render the earlier allegation of sexual assault less remote and also as evidence itself suggestive of the landlord’s sexually aggressive tendencies.
¶12(a) The landlord’s forty-nine year old girl friend
¶13At the first trial, evidence of the seven year old allegation and the women’s lingerie and photographs had also been excluded. When the rulings were challenged on appeal, we held in Conkey I that it was not error to refuse to admit evidence of the seven year old sexual assault: “[t]he points of similarity between the present case and the crime allegedly committed by the victim’s landlord are few.” Commonwealth v. Conkey, 430 Mass. 139, 146 (1999). Likewise, we held it was not error to exclude testimony that women’s nylons were found in the landlord’s residence: “There was no connection between those nylons and that used as the ligature on the victim.” Id. at 147. (The exclusion of the photographs found in the landlord’s home was not challenged on appeal.) At the second trial, this same evidence was excluded once more as well as the new evidence about the landlord’s sexual aggressiveness. The judge’s reasons for excluding the evidence at the second trial were that the 1987 allegation of sexual assault was “too remote in time” and that there was a “fundamental lack of similarity between all of these matters on the one hand, and the death of [the victim] on the other hand.”
¶14Given our decision in Conkey I, we do not fault the judge for excluding the proffered evidence. However, at the second trial, the defendant made a greater showing that the landlord had the opportunity to kill the victim (through the testimony of his fiancée, which had not been introduced in the first trial); that he exhibited consciousness of guilt (the landlord’s conversation *69with the tenant at 917 before the body was discovered in which the landlord suggested that the victim might have gone to California); and that the assault on the victim was part of a pattern of his sexual aggression against women who had rejected him.
¶15We analyze the judge’s reasons for excluding the evidence in terms of the newly offered evidence. The judge stated that the evidence of the 1987 sexual assault was “too remote in time.” While the original allegation of sexual assault had been distant at the time of the first trial, at the second trial, the defense offered evidence of several more current similar allegations that portrayed a pattern of sexually aggressive acts continuing until several months before the murder. The later acts rendered the seven year old one relevant, and were themselves relevant as part of a pattern. The judge’s other reason for excluding the evidence of the prior sexual incidents was that he perceived “a fundamental lack of similarity between” the proffered evidence and the murder. In this regard, he may have been led astray by our comments in Conkey I that “the primary motive appeared to be burglary and larceny” and “[b]y contrast, the prior crime alleged to have been committed by the landlord was a sexual assault with evidence of rape and the taking of sexually explicit photographs.” Conkey I, supra at 146-147. Although the “primary” motive for the murder may have been burglary, there was evidence (at both trials) suggestive of a sexual assault as well. Despite the lack of scientific evidence of sexual assault, the facts that the victim’s pajama bottoms were found on her bed and her panties on the floor, and that her pajama top had been ripped open with one of its buttons forcibly removed and lying on the bed and another button missing, provided sufficient evidence that a sexual assault may have been involved. Indeed, in the first trial the Commonwealth indicted the defendant for assault with attempt to rape in connection with the murder. He was tried on the sexual assault offense and, after the jury were deadlocked, the Commonwealth nol pressed this indictment. Thus, at least at one time, the Commonwealth clearly viewed the scene as one indicative of an attempted sexual assault.
¶16In view of the additional evidence offered by the defendant in this trial regarding the landlord’s sexual aggression toward *70women, it simply cannot be said that the evidence of the landlord’s prior incidents of sexual assaults was not relevant. This additional evidence provided sufficient similarity between all the prior incidents and the present crime to render the proffered evidence relevant. The evidence assumes even greater relevance given the fact that, according to the defendant, he had no connection with the victim. By contrast, the landlord had a relationship with the victim, possessed a key to her home, had been in her bedroom recently and even had opened her lingerie drawer. He had a history of sexual assault and anger when rejected by women and he had been rejected by the victim here. There was substantially more evidence of motive on the part of the landlord than on the part of this defendant.
¶17Based on the totality of the showing here, we conclude that the new evidence altered the equation, tipping the balance in favor of admission, and that the defendant was denied his right to present evidence that another committed the crime.
¶18*712. Defendant’s refusal to give written statement to police. The defendant contends that evidence that he refused to provide a written statement to the police should not have been admitted and requires reversal of the convictions. Captain Stephen Corr of the Lexington police department testified that, on December 29, the defendant gave the police his account of the events on the night of December 3-4, and retraced for them the route he had taken that night. The police then asked the defendant to go to the station to reduce his statements to writing, and he refused to do so. As the Commonwealth began to introduce this evidence, the judge, sua sponte, alerted defense counsel to the problems of such testimony and defense counsel specifically stated that he did not object to such evidence. Now, the defendant maintains that the evidence that he refused to accompany the police to the police station to provide a written statement violated his right against self-incrimination. Because we reverse on other grounds, it is unnecessary to consider whether, despite the defendant’s affirmative choice not to object, the admission of the statement was error that created a substantial likelihood of a miscarriage of justice.
¶19The defendant’s refusal to provide the police his fingerprints was the basis for the reversal of the convictions after the first trial. See Conkey I, supra at 141-143. Testimony of the defendant’s refusal to give a written statement is no more admissible than was the evidence of his refusal to provide fingerprints. The defendant was forced to choose between “two potentially inculpatory alternatives” (either providing a written statement or having evidence of his election not to do so placed before the jury). See Conkey I, supra at 143. Cf. Commonwealth v. Delaney, 442 Mass. 604, 607-612 (2004). Thus, his refusal to comply with the police request may not be introduced against him over objection without violating art. 12. See Conkey I, supra at 143. The Commonwealth contends that the evidence was necessary to present a complete picture of the investigation; to combat the second prong of the defense, that the police investigation was not thorough; and to demonstrate that the defendant’s statements to the police were voluntary. The *72evidence is not needed to present a complete picture of the investigation. Every step that the police did not take need not be presented or explained. There was extensive testimony of the details of the investigation. Imperfections can always be probed, as they were here. But even if these reasons for admitting the evidence were valid, they do not overcome the defendant’s right to be protected from incriminating himself.
¶20The defendant also argues prejudice from testimony that the police obtained his fingerprints from “another agency.” The fact that the fingerprints were obtained from an “agency” suggests that it may have been a law enforcement agency. The source of the fingerprints is of no relevance, and in a retrial should be omitted.
¶213. Denial of motions for required findings. The defendant contends that the Commonwealth did not present sufficient evidence that he murdered the victim; rather, the only evidence was that he broke into her home after her death.. If so, the defendant would be entitled to judgment, not merely a new trial. We review to determine whether the evidence viewed in the light most favorable to the Commonwealth could have “satisfied a rational trier of fact” of each element of the crimes charged beyond a reasonable doubt. Commonwealth v. Latimore, 378 Mass. 671, 677-678 (1979). Inferences from the evidence “need only be reasonable and possible; [they] need not be not necessary or inescapable.” Commonwealth v. Lodge, 431 Mass. 461, 465 (2000), quoting Commonwealth v. Bush, 427 Mass. 26, 30 (1998). Circumstantial evidence may be competent to establish guilt as long as it is sufficient to establish beyond a reasonable doubt that the defendant, and not someone else, was responsible for the killing. See Commonwealth v. Merola, 405 Mass. 529, 533 (1989). The Commonwealth need not prove that no one else could have committed the crime. See id. See also Commonwealth v. Anderson, 396 Mass. 306, 311-312 (1985), citing Commonwealth v. Casale, 381 Mass. 167, 175-176 (1980).
¶22The defendant, who did not own a car, lived within walking *73distance of the victim’s home. He telephoned his workplace at 10:41 p.m. on the night of the murder, to report that he would be unable to work the following morning. He was an admitted burglar who “liked” breaking into homes when they were occupied. Evidence suggested that the murder occurred during a burglary: jewelry was out of place on the victim’s vanity and strewn on the bedroom floor, and her two purses were missing. The jury could permissibly conclude that the disturbed jewelry indicated that on being discovered, the defendant decided to kill the victim. The victim suffered seven blows to her head with a blunt instrument, and the defendant admitted to his girl friend that he entered the home in possession of a flashlight.
¶23The defendant’s account of his reason for entering the home and his actions therein had many inconsistencies and was contradicted by other evidence. He told the police that he was smoking a cigarette near the victim’s home, heard a scream that lasted “several seconds,” believed that it came from the victim’s home and that it might be “domestic” violence, so he went in to see what had occurred. None of the other neighbors, even those who lived quite close to the victim and heard the sound of glass breaking, heard a scream at about this time.
¶24There was also substantial consciousness of guilt evidence. While such evidence alone may not support a verdict of guilt, it may be considered along with all other evidence. Cramer v. Commonwealth, 419 Mass. 106, 111 (1994). When questioned by the police, the defendant repeatedly denied ever being in the victim’s house.
¶254. Admission of evidence that the defendant watched people visiting stores across from his house. The defendant claims that the judge erred in permitting a neighborhood resident to testify that the defendant would stare at her as she waited at the bus stop in front of his house, and that she changed her walking pattern and visits to the local stores because she saw him watching her. The defendant argues that this evidence was a “tainted combination of prior bad act and character evidence.” These contentions were rejected in Conkey I: “The testimony was relevant to show that the defendant was familiar with the victim and to impeach his credibility in his statements to the police . . . [t]he judge committed no error in admitting the evidence.” Con-key I, supra at 146. The defendant argues that the testimony should not have been admitted at the second trial because this time his objections were more “specific[]” and because there was stronger evidence of the landlord’s culpability. The Commonwealth’s evidence may be presented differently at a retrial and thus we do not pass on what is presently an abstraction.
¶265. Defendant’s motion for funds for forensic testing on a note *75and on hairs. The defendant claims that the judge should not have denied his postconviction motion for funds for forensic testing. He sought the money to have tests performed on hairs that had been found on the victim’s pajama top and on the bloodstain on the note written by the victim on November 28.
¶276. Denial of second motion to suppress without hearing. Before the first trial, the defendant moved to suppress statements made to his girl friend, Barbara Tucker, on the ground that she was acting as a government agent. The motion was denied. Prior to the second trial, the defendant’s investigator spoke with Tucker, and the defendant submitted a report of the investigator’s conversation as the basis for the defendant’s second motion to suppress on the same grounds.
“The court, however, does not find that Barbara Tucker was ever asked to visit the defendant, nor was she asked to obtain information from the defendant. ... In fact, in the recent affidavit submitted by the defendant, Tucker maintains that the police never specifically requested that she ask [the defendant] any questions, and that the police even discouraged her from visiting him.”
¶28“A motion judge has discretion to act on a request for rehearing without conducting a [further] hearing if the defendant has raised no new issues and the relevant law has not changed.” Commonwealth v. Cryer, 426 Mass. 562, 569-570 (1998). The same principle applies where the motion is reasserted prior to a retrial. The motion judge did not abuse her discretion. The defendant posits that an evidentiary hearing would have demonstrated that Tucker was acting as a government agent when, with police knowledge and implicit encouragement, she elicited information from the defendant during a prison visit. *76The defendant relies primarily on his investigator’s report describing the conduct of a police officer who allegedly elicited information from Tucker in a flirtatious manner, gave her false inculpatory information about the defendant, and tacitly gave her the “go ahead” to elicit statements from the defendant. However, even considering the investigator’s report as an affidavit, the judge was warranted in her conclusion that any new information did not affect the fact that Tucker was not asked by the police to obtain information from the defendant or to visit him; indeed, the police sought to discourage her from seeing him.
¶297. Closing argument. The defendant claims that the prosecutor improperly suggested that a dog was the source of the hairs found on the victim’s pajamas and that therefore the government had done “everything possible to rule out [the landlord] as the true killer.” The language at issue is set forth in the margin.
¶308. Merger and duplicative convictions. The defendant argues that the armed assault in a dwelling conviction merges with the murder conviction and must be vacated because the assault was not independent of the homicide; rather, he claims that the assault was part of the homicide. The defendant also maintains that the underlying felonies of armed assault in a dwelling and armed burglary were duplicative of the felony-murder conviction and must be vacated. We need not address these claims, as any issue of merger or duplicative convictions may be addressed should there be such convictions on retrial.
¶319. Other issues. We briefly discuss the defendant’s other arguments that may be material at any retrial.
¶32(a) The defendant states that the prosecutor asked the jurors to “imagine themselves in the victim’s shoes” by using the *77word “your” in his opening statement: “This case is about the heart [sic] of being woken in the middle of the night, in the security of your own home, in the comfort of your own bedroom by a stranger and being assaulted and beaten and strangled by that stranger, all because the stranger was trying to steal a few valuables and got caught in the act.” The word “your” was used in a general sense, to summarize the plight of the victim; here it did not invite the jury to place themselves in the victim’s position, (b) The defendant argues that the felony-murder instruction suggested that conviction of such charge carries a life sentence. As the defendant concedes, the judge instructed the jury in accordance with the Model Jury Instructions on Homicide 15 (1999). His instruction that a felony-murder conviction requires the Commonwealth to prove that the defendant committed or attempted to commit a felony with a maximum sentence of life imprisonment was correct and merely restated one of the elements necessary for a conviction of felony-murder, (c) The defendant claims that the judge erred by not conducting, sua sponte, a voir dire on the voluntariness of the defendant’s statements to the police on December 29 pursuant to the “humane practice” role. See Commonwealth v. Tavares, 385 Mass. 140, 149-150, cert. denied, 457 U.S. 1137 (1982), and cases cited. No voir dire was necessary. “[A] judge is obliged sua sponte to conduct a voir dire only where there is evidence of a substantial claim of involuntariness, . . . and where voluntariness is a live issue at the trial.” Commonwealth v. Stroyny, 435 Mass. 635, 646 (2002), and cases cited. Voluntariness was not a live issue here. Moreover, the defendant rejected the judge’s many offers to give a “humane practice” instruction because the defense strategy was to convince the jury to believe the defendant’s statements to the police and thus believe that the defendant entered the house only after the murder, (d) The defendant maintains that the judge should have granted him a second evidentiary hearing on his motion to suppress his statements to the police on December 29 on the ground that he had new evidence that the police violated his rights under the Fourth Amendment to the United States Constitution when they interviewed him without providing him Miranda warnings. An evidentiary hearing on this issue was held prior to *78the first trial. The motion was denied and we concluded in Conkey I, supra at 144-145, that, in the circumstances, Miranda warnings were not required. Prior to the retrial, the defendant sought rehearing of this issue. He submitted an affidavit stating that a police officer had placed his foot across the threshold of the defendant’s apartment when the defendant had attempted to close the door. The judge who reviewed the affidavit reasoned that it was “unquestionable that a significant happening such as a show of force by the police would not have been forgotten . . . or originally left unmentioned .... The defendant. . . had ample opportunity to raise the issue of force used by the police both in his previous affidavit, the pretrial hearing and the appeal, but he never did.” No new questions of law were raised and the motion judge was warranted in discrediting the defendant’s affidavit. See Commonwealth v. Cryer, 426 Mass. 562, 569-570 (1998). The motion was properly denied without an evidentiary hearing.
¶33The judgments are reversed, the verdicts set aside, and the cases remanded to the Superior Court for a new trial.
¶34 So ordered.
¶35A mistrial was declared on an indictment charging assault with intent to rape after the jury reported they were deadlocked. This indictment was later the subject of a nolle prosequi. See infra.
¶36The other button was never located.
¶37The record does not reveal precisely where these hairs were found. There was testimony that the victim had a cat. There was no evidence whether either the defendant or the third-party culprit had a pet.
¶38The police had previously interviewed the defendant during routine interviews of all neighbors.
¶39The defense also attacked the completeness of the police investigation.
¶40By the time of trial, the landlord had moved to Oregon. When the defense sought to call him as a witness, he invoked his right against self-incrimination in a telephone call.
¶41There was no objection to this conversation (which was elicited by the defense) and the words were apparently offered not for their truth, but for the fact that they were spoken.
¶42This note had a drop of blood on it. The Commonwealth discontinued previously ordered tests on the blood. (Because the note had been written by the victim and was in the landlord’s possession when he was making repairs, identifying the blood on the note as belonging to either of them would not have been significant. See discussion, infra.)
¶43The police found the note the landlord had written the victim in a kitchen wastebasket in the victim’s home.
¶44In a search of the landlord’s home conducted pursuant to a search warrant on December 7, the police found keys to 915 and 917 Massachusetts Avenue in his dungarees.
¶45The landlord later provided the police with a written statement of his activities at the pertinent times.
¶46The witness was not certain whether the landlord told her this directly or she had heard it from a colleague.
¶47The lingerie and photographs were seized by the police pursuant to a search warrant.
¶48The statement in Commonwealth v. Conkey, 430 Mass. 139, 146 (1999), that “[w]e do not. . . disturb a trial judge’s decision to admit or reject [evidence that another person recently committed a similar crime by similar methods] unless justice requires a different result,” suggests the independent scrutiny applied by appellate courts when constitutional decisions are involved and is an implicit adoption of a standard higher than that of abuse of discretion.
¶49Implicit in an offer of proof is the representation that the evidence is available and admissible.
¶50As mentioned earlier, the victim in the present case was also forty-nine years old.
¶51The judge at any retrial, will, of course, exercise normal discretion with respect to any third-party culprit evidence actually offered. Our conclusions are based only on offers of proof. That is, any evidence of a third-party culprit will have to meet the normal admissibility requirements. In addition, depending on the precise admissible evidence offered, some of the evidence discussed as prior sexual activity may be irrelevant and therefore inadmissible. For example, the testimony of one woman that the landlord treated his dates as “slave labor” and forced them to do yard work becomes significant only when offered in conjunction with the other testimony about the landlord’s sexually aggressive tendencies. By itself, such evidence would be meaningless and irrelevant.
¶52The defendant also contends that his additional evidence of the landlord’s sexual activities should have been admitted to rebut the testimony of two women that the landlord was “nice,” “pleasant,” and “cordial.” In view of our decision, we need not address whether such testimony alone would be suf*71ficient to require admission of evidence about the landlord’s sexually aggressive behavior.
¶53We note that here the defendant specifically rejected the judge’s offer to instruct the jury not to draw any “inference adverse to the defendant” from the fact that the police obtained his fingerprints from “an agency.”
¶54Two neighbors (sleeping in the same bedroom) testified to being awakened by the sound of glass breaking between 11:30 p.m. and midnight on December 3, and they “usually” kept the window open slightly. Another neighbor heard the sound of glass breaking outside between 1 a.m. and 2 a.m. on December 4.
¶55He did state to his girl friend that he “saw a shadow” in the house.
¶56It would be logical for a housebreaker to fear any such involvement, but the inconsistent statement nevertheless is evidence that the jury could consider.
¶57The landlord gave this note to the police.
¶58The investigator’s report was treated as an affidavit. See Mass. R. Crim. P. 13 (a) (2), 378 Mass. 871 (1979).
¶59“Those hairs. All this stuff about hair. Remember what Agent Hopkins said? It’s a dog hair. Dog hair. She did not have a dog. How did a dog hair get in there? Just like those other hairs could have gotten there. Agent Hopkins, ‘I expect, in examining a crime scene, to find hairs that are not disassociative,’ or whatever big word he used. I can’t even say it. Non-issue, I suggest, ladies and gentlemen.” (Emphasis added.)