Mich. Comp. Laws § 600.4364

Sec. 4364. No person who has been discharged by the order of any court or judge upon habeas corpus shall be again restrained for the same cause. It is not the same cause if: (1) He was discharged from a commitment on a criminal charge, and is afterwards committed for the same offense, by the legal order or process of the court wherein he is bound by recognizance to appear, or in which he is indicted or convicted for the same offense; or (2) After a discharge for defect of proof, or for any material defect in the commitment, in a criminal case, the prisoner is again arrested on sufficient proof, and committed by legal process for the same offense; or (3) In a civil suit the party was discharged for any illegality in the judgment or process and is afterwards imprisoned by legal process for the same cause of action; or (4) In any civil suit in which process may lawfully issue against the body, he was discharged from commitment on original process, and is afterwards committed on execution in the same cause, or on original process in any other suit, after such first suit was discontinued.