Yes, Kentucky and Ohio are reciprocal states. You will need to file a KY resident tax return and an OH non-resident tax return.
Just be sure to fill out your Personal Info correctly during the program interview; i.e., that you are a resident of Kentucky, and that you work in Ohio.
Also, when completing your state tax returns, be sure to finish the non-residential return first (Ohio), and then the residential return second (Kentucky). Doing this will insure that KY will give you credit for any tax that your employer withheld in Ohio.
In the future...
"A reciprocal agreement, also called reciprocity, is an agreement between two states that allows residents of one state to request exemption from tax withholding in the other (reciprocal) state. This can save you the trouble of having to file multiple state returns.
If your employer has withheld taxes for the work state instead of the resident state, you'll have to file for a refund from your work state. You'll still file your resident return that also includes that income and pay tax on it.
TurboTax handles reciprocal states and will generate the correct state(s) based on your personal information and your W-2."
"As a worker in a reciprocal state, you can fill out that state's exemption form and give it to your employer if you don't want them to withhold taxes for your work state. If you do this, make sure your employer also withholds taxes for your resident state, otherwise you may get hit with underpayment penalties come tax time."
Ohio Department of Taxation - Employee’s Statement of Residency in a Reciprocity State
For more information, please see TurboTax FAQ: What is a state reciprocal agreement?
For more information, please see TurboTax FAQ: Which states have reciprocal agreements?
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