No actual "battle" occured within the county that I can find, but there was some activity - as with every county in Missouri.
In researching my great-great-grandfather's civil war role, I've found he served from 37-39 days active duty in Captain Peter Thompson's Company C with the 45th Enrolled Missouri Militia between August & November 1862. The time was spent guarding the unit's armory of rifle-muskets (probably kept at the courthouse), assisting the provost marshal to arrest suspected disloyals, some patroling, and fighting with guerrilla leader Bill Dunn's band in the area. 30 men of the 45th EMM garrisoned in Unionville all that summer.
Again in 1864 he was called into Captain G.W.R. Ledford's Company E to go to Macon County to help thwart any threat on the Union District Headquarters in Macon City when Sterling Price was pushing northward with 11,000 men in September-November 1864.