[edited: Mar. 6, 2016, 8:41pm]
Ohio and Kentucky have a reciprocal agreement. This means that if you live in one of these states but work in the other, you'll only need to file a return for the state in which you live.
Therefore, you'll need to file a Kentucky State Return.
If the only Ohio based income you had was from your employer, then no you do not have to file an Ohio return. Ohio makes an exception to their filing requirement, in this case, if you live in a boarding state.
For more information on State Reciprocal Agreements:
https://ttlc.intuit.com/replies/4776822
