If it is owned and controlled by any Kentucky government then yes. Kentucky law states only Kentucky and the Federal government can regulate carrying firearms on government property in the state. They can prohibit CC in buildings but they cannot completely bar you from carrying a weapon.
If it is a private business they can prohibit firearms on their property but signs do not have the weight of law. If they ask you to leave because of your firearm (or any other reason) and you refuse then you are trespassing, but if you just ignore or don't see a sign then you're just breaking their rules.
For a cite see the thread entitled Kentucky Gun Laws.