You may be interested in this reply I made to a similar question a couple months ago. It also has a link to a few related threads too.

During the American Civil War, a large number of native Americans served in both the Union and Confederate armies. Civil War historians (with scholarship in native American tribes), like Gaines and Hauptman, have estimated about 20,000 native Americans having enlisted in one or the other army.

During the Civil War, native tribes also came into conflict with both Federal and Confederate forces in the Midwest and West, though the relatively small number of occupying soldiers meant conflict was low intensity and isolated. The Apache, Comanche, and Sioux numbered among the major tribes engaging in skirmishes and raids, which in context were opportunistic but generally disinterested in the politics of the Civil War. The biggest impact is arguably that of the Comanche in Texas, who took great advantage of the inability of Confederate forces to properly maintain the frontier.

Tribes in the East, however, took more of a political interest in the outcome of the war as they recognized that the victory of one or another belligerent would likely impact their own prospects. These tribes, or members within a tribe, aligned themselves accordingly.