Here is information of the regiments activities. If you could get access to Broadfoot’s Supplement to the Official Records, you could possibly view the companies record of events for it’s entire existence. These volumes are available in many of the larger libraries.
http://en.wikipedia.org/wiki/10th_Michigan_Volunteer_Infantry_Regiment
See also:
http://www.tenthmichiganinfantry.com
http://www.youtube.com/watch?v=qvY6QLctGeI
http://www.youtube.com/watch?v=Tu1InKcwF1I
http://www.civilwararchive.com/Unreghst/unmiinf2.htm