Mustered into service as a Private on July 29th, 1861
Private Osborne was discharged from the 19th Indiana for disability in December of 1861.
On August 21st, 1862 a man with the exact same name mustered into Company H of the 101st Indiana Infantry. This soldier died on December 27th, 1862 while in Munfordsville Kentucky and is buried at the Cave Hill National Cemetery located in Jefferson County Kentucky.
It is very likely that this is one in the same person. Currently there is no evidence to support this guess.