No, you will not need to file in Ohio. Kentucky and Ohio are reciprocal states, which means they have an agreement that you only pay state taxes where you live. To ensure that the Ohio return is not generated, simply answer no to the question if you lived or worked outside of Kentucky. Because of the reciprocal agreement, you are not considered to have worked in Ohio.
Here is an FAQ on reciprocal agreements: https://ttlc.intuit.com/replies/4776822
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