If there is no OH withholding in box 17 of your W-2, you do not need to file an OH return.
OH & KY do have a reciprocal agreement. So. if OH tax was mistakenly withheld, you do need to file an OH return to get it refunded. KY will not give you a credit for tax mistakenly paid to a reciprocal state (as one of the other replies indicates)
