Jim,
I'm not sure what the 3rd Inf State Troops are in terms of State Organization. My Great Grandfather, Lt. James T. Clarke was captured at Vicksburg on July 4, 1863 as a member of the 3rd Bn, MS State Troops commanded by Lt. Col Burgin. I have his complete record including the surrender document. I'm sure you have seen the web site http://www.mississippiscv.org/MS_Units/minute_men.htm which also discusses the State Troop by the SCV. Hope this helps.