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
I understand that part but I have this issue. I am a travel nurse that lives in KY. I did travel assignments in KY and OH. My travel company took money from me to pay KY, Ohio and Nebraska (where THEIR office is) in error. What do I do now for taxes? I should have that money refunded since I shouldnt have paid those states. Correct?
@shayschrode --
Your home state of KY can tax all your income, regardless of where you earn it. Therefore your employer was correct to withhold KY taxes.
KY and OH have tax reciprocity for W2 income. Assuming your income is reported on a W2, see Question #2 on this OH webpage for the procedure to follow to obtain a refund. Your W2 income is not taxable by OH.
https://tax.ohio.gov/help-center/faqs/employer-withholding-refunds/employer-withholding-refunds
If you never actually worked in Nebraska (or as a telecommuter for a NE-based employer), your income is not subject to Nebraska income tax. To obtain a refund, you must file a non-resident NE tax return on which you show the NE withholding but allocate zero income to NE. This should result in a full refund from NE.