In order to receive a refund of the incorrectly withheld OH STATE income tax, you'll have to file a non-resident OH tax return at year's end. Be advised that Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT) does this by allocating your income as either Ohio or non-Ohio. W-2 income will be allocated by the state name abbreviation shown in box 15 of your W-2. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income. Make sure that your non-Ohio wages show PA (Other state postal abbreviation) in box 15 of your W-2 screen, with the PA amount in box 16.
If you are a regular remote worker (as opposed to temporary during covid*), your employer should not have withheld local tax. You will have to file a separate city return to claim that refund. Contact the city tax dept. for instructions**, many have a special form for this situation. After confirming with the city that you are entitled to a refund, try again to convince your employer they should not be withholding city tax. The reciprocity agreement, between PA & OH does not apply to city tax. You would not be entitled to a refund if you physically worked in that city.
*Ohio, passed HB 197 which basically says working from home due to the COVID-19 pandemic shall be deemed to be a day performing personal services at the employee’s principal place of work. So you still need to pay city income tax to the city where the employer is located.
**For a list of all Ohio cities with an income tax go to http://www.tax.ohio.gov/municipalities/municipal_income_tax_forms.aspx
From there, there is a link to each city’s web site and/or RITA / CCA
