Same as birth, see above. Cost at county level not known. 717 Allegan Street Lansing, MI 48909 Information before 1867 must be obtained from the local county or township clerk. It is strongly recommended to consult the Redbook and making a few phone calls before mailing or driving. Also, since privacy laws are more restrictive for birth records than death records, it is strongly recommended obtaining a death record and using this as evidence of death in requesting a birth record.
Privacy laws protect the living.
It seems to me that if you can prove that the person is dead, you have a better chance of getting a birth record. Their headquarters are in Salt Lake City UTAH where all records are kept. Throughout the US are LDS Family History Centers, facilities to assist genealogists and other interested persons in their quest for ancestors. The Mormon Library has a surname index which lists the surnames of which a genealogy is already in existence. These last two indexes are also available from most large metropolitan libraries.