Michigan Compiled Laws, Chapter 552. Divorce § 552.31

Sec. 31. When a marriage is dissolved on account of a prior marriage of either party, and it shall appear that the second marriage was contracted in good faith, and with the full belief of the parties that the former wife or husband was dead, that fact shall be stated in the decree of divorce or nullity; and the issue of such second marriage, born or begotten before the commencement of the suit, shall be deemed to be the legitimate issue of the parent who, at the time of the marriage, was capable of contracting.