Ohio has a reciprocal agreement, on wages, with all neighboring states. No Ohio state taxes are withheld or due and you do not need to file an OH return. But your home state will tax you on your Ohio income.
If Ohio taxes are mistakenly withheld, you have to file an Ohio return to get a refund. You should ask your employer to stop withholding so you don't have to file an Ohio return every year.
However the reciprocity agreement does not apply to local city taxes. You are not required to file a local city return, but you are also not entitled to a refund of the city withholding, unless there was an error in the amount
