Although the Civil War produced some very interesting weapons & some had complex actions but I know nothing of a bolt action rifle/carbine produced during the war.
The earliest (that I know of) U.S. bolt action rifle /carbine was mnfg. in the early 1870's called the Ward Burton & issued on a test basis. Never proved popular among the troops. The 7th had a few carbines issued & there have been rumors that some were at the LBH but that has never been proven.
The next bolt action was the Krag that came along in the 1890's & was successful.