If you can identify pertinent Michigan units. A good place to find soldier’s diaries, letters, etc., is the U. S. Army Military History Institute, Carlisle Barracks, Pa.

They hold in their unit bibliographies many such documents, see

Reference Bibliographies - US Army Heritage and Education Center
http://cdm16635.contentdm.oclc.org/cdm/landingpage/collection/p16635coll9

Better yet, a visit there is well worth your while

Here’s an example

10th Michigan Cavalry Regiment

The following pertinent personal papers are in the Institute’s Manuscript Archive:

Peavy, A. F. - LighColl-Bk 42:57 (Enlisted man’s discharge, Nov 11, 1865)

……….........................................

Adelbert F. Peavy

Residence MI; 18 years old.
Enlisted on 9/3/1863 at Hamburg, MI as a Private.
On 10/2/1863 he mustered into "K" Co. MI 10th Cavalry
He was Mustered Out on 11/11/1865 at Memphis, TN
Promotions:
* Bugler
After the War he lived in Howell, MI

Sources used by Historical Data Systems, Inc.:
- Record of Service of Michigan Volunteers 1861-65