No. It's already done. The reciprocity
agreement, between OH & KY, on state taxes, does not apply to local city and county taxes. You can not
get the amount in box 19 refunded, but you do not have to file a KY local return (the local KY tax is most likely city or county tax, not school district).
If you live in an Ohio city with an income tax, they may give you a
credit or partial credit. Many do. You
need to check with your city. If you live in an Ohio School District with a tax, you can NOT get a credit for the box 19 amount.
