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
This resource has brief summaries of the records of Michigan soldiers in the Civil War, typically including, but not limited to, name, rank, company and regiment, branch of service, date of enlistment, age at enlistment, promotions, and date of discharge or date of death. It is both searchable and browseable, but it is most helpful to know the branch of service and regiment of the soldier, if browsing. The particular source I used to search for soldiers in the Second Michigan Cavalry was volume 32 in the above series, two copies made available by the University of Michigan, and another, by Michigan State University. This is one of the University of Michigan copies, with link):
Record of Service of Michigan Volunteers In the Civil War, 1861-1865, Vol. 32. Michigan, Adjutant-General’s Dept. (Kalamazoo, Mich.: Ihling bros. & Everard, printers, 190-), Hathitrust Digital Library, babel.hathitrust.org.
Link to Volume 32 (not sure it will work, no permanent link was given):
The same resource is searchable on Ancestry.com, though I noticed that the search mechanism doesn't seem to retrieve results well with the soldier's given name--just the surname. This link is to a catalog of all volumes in the series: