Despite northern fears and southern hopes, Kentucky did not secede from the Union. At the beginning of the war, it seemed as if they very well might, but Kentucky was severely divided and adopted an official policy of neutrality, demanding that both Union and Confederate forces stay clear. This obviously couldn't last very long; it was a question of who would move first, and the Confederacy obliged the Union. When Confederate General Leonidas Polk occupied Columbus in September 1861, it effectively pushed Kentucky into Union hands. Confederate sympathizers established a shadow government, initially based at Bowling Green, but soon displaced to the Confederacy after the occupation of the state by Union forces. Braxton Bragg invaded Kentucky in summer-fall 1862 with the intention of liberating Kentucky, which Confederates had deluded themselves into believing to be ripe for the picking, but he was met by a notably cool reception, and was soon forced to withdraw back into the Confederacy proper.
With that said, some white Kentuckians did cross the border and join the Confederacy, forming the so-called Orphan Brigade of the Army of Tennessee. Significantly more - especially black Kentuckians - fought for the Union.