It depends. Did you only have state withholding from KY on you paycheck? If you are a Kentucky resident, you won't file Form 740 NPR (that form is for non-residents of KY). TurboTax creates the correct state tax returns based on your entries in the Personal Info Section and your W-2.
Kentucky and Ohio have reciprocal agreements, which means that if you live in either state and work in the other state, you only need to file a state return in the state that you live in. You have to complete Form IT-4NR so your employer won't withhold state taxes for OH. If you didn't fill out that form, and your job withheld state taxes for OH, you should get a refund, but you will have to pay your taxes for Kentucky.
Refer to the TurboTax Help articles What is a state reciprocal agreement? and Which states have reciprocal agreements? for more information.