No, these are just taxes that were paid to the OH locality were you worked and do not get reported on your federal or KY resident state income tax returns.
The
KY - OH reciprocity agreement does not apply to local city income taxes. You
are not required to file a local OH city tax return, but you are also not
entitled to a refund of the city withholding, unless there was an error in the
amount.
KY localities
only collect KY city income taxes for work done in that KY locality so if
you did not pay any KY city income taxes, you will not be able to be claim
a city income tax credit in your KY locality related to your OH city income
taxes paid on your OH sourced income.
