Maybe this info will help you decide if this is your ancestor.
According to the compiled service record at Footnote.com (now known as Fold3.com)
Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Missouri (NARA) Thomas Conner enlisted as a Private on January 13, 1862 in (Old) Company "D" 2nd Missouri Infatry (which later became the Company "K" 3rd regiment Missouri Infantry) at Greene County, Missouri for 1 year of service. On Mar/Apr 1862 muster roll he is absent, left sick at hospital at Elk Horn, Arkansas on March 10, 1862. No further record.