Okla. Stat. tit. 21, § 871

Adultery is the unlawful voluntary sexual intercourse of a married person with one of the opposite sex; and when the crime is between persons, only one of whom is married, both are guilty of adultery. Prosecution for adultery can be commenced and carried on against either of the parties to the crime only by his or her own husband or wife as the case may be, or by the husband or wife of the other party to the crime: Provided, that any person may make complaint when persons are living together in open and notorious adultery.