I know there were Ky units fighting for both sides at Murfreesboro, TN - do you know if they fought directly against each other though? I got that impression from somewhere, but it's a hazy recollection...
The largest battle fought in Kentucky, Perryville, had a large number of Kentuckians on the Union side, but only a few companies of Kentucky cavalry on the Confederate side. Most of the Confederate Kentuckians were down in Mississippi with Maj. Gen. Breckinridge's Corps. He did not get along with Gen. Bragg, the Confederate commander of the invasion of Kentucky, so his force was sent down to fight at Baton Rouge.