Yes, you can deduct the local taxes paid to Ohio on your itemized deductions.
If there is no state withholding for Ohio then you do not have to file an Ohio return. File your Kentucky resident return.
Kentucky and Ohio
have a reciprocal
agreement when it comes to wages. Ohio recognizes you are a
Kentucky resident and they do not require you to pay any tax on your wages. If there were any Ohio state tax withheld by your employer you would file only to receive a refund.