The reciprocity agreement between IN & KY does not apply to local city or county taxes. You are not required to file a county return (part of the IN state forms), but you are also not entitled to a refund of the county withholding (box19 on your W-2), unless there was an error in the amount. If you are subject to a KY county or city tax, you should check to see if the KY city will give you a credit for the IN county tax withheld. KY does allow an itemized deduction (Schedule A) for local tax paid, on the state return.
Be aware that @Hal_Al 's answer applies only to salary or wage (W-2) income. if you have any other kind of IN-source income (for example, rental income from a property located in IN), you'd have to file a non-resident IN return.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
Correct, the state reciprocal agreement only applies to W-2 wages. I assumed that "We pay local taxes only" meant that there was local withholding in box 19 of poster's W-2.