Ohio has a reciprocal agreement, on wages (you get a form W-2), with all neighboring states. No state taxes are withheld or due and you do not normally need to file a return for the other state (MI, PA, KY, WV, IN). But OH will tax you on your other state income.
If PA taxes are mistakenly withheld, you then have to file a PA return, to get a refund. OH will not give you a credit. You should ask your employer to stop withholding so you don't have to file a PA return every year. If you work in Pennsylvania but are a resident of Ohio, submit PA exemption form REV-419 to your employer. Your employer may or may not be willing to withhold OH tax instead.
However the reciprocity agreement does not apply to local city taxes. You can not get those refunded. But if you live in an Ohio city with a tax, they may give you a credit or partial credit. Many do. You need to check with your city.
If you are self employed, the reciprocity agreement does not apply. You will have to file a PA return. But, OH will give you a credit for what you pay PA (you will probably claim the OH Business Income Deduction instead of the credit).
