Record of service of Michigan volunteers in the civil war, 1861-1865.Record of Service of Michigan Volunteers (PDF online)
Pub. by authority of the Senate and House of representatives of the Michigan Legislature under the direction of Brig. Gen. Geo. H. Brown, adjutant general.
Hathitrust has many more volumes than the ones selected below. My links may provide clues. For instance, Volumes 1-30 are Michigan Infantry units; Volume 31 begins the First Michigan Cavalry (etcetera). Besides this series, the site has links to other series. I noticed a volume somewhere on the Michigan Pioneers, and there may be volumes on the drafted regiments).
Volume 01, First Michigan Infantry
Volume 22, Twenty-Second Michigan Infantry
Volume 30, Thirtieth Michigan Infantry
Volume 31, First Michigan Cavalry
Volume 32, Second Michigan Cavalry
Volume 36, Sixth Michigan Cavalry