You have to file an Ohio part year resident return.
It may first appear that Ohio is taxing all your income, but it isn't.
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 TN (Other state postal abbreviation) in box 15 of your W-2 screen, with the TN amount in box 16.
Since TN does not have an income tax, boxes 15-17 may be blank on your actual W-2. At the W-2 screen, in TT, enter TN in box 15. Put the box 1 amount in box 16 and 0 in box 17.
This system allows Ohio to apply their highest tax rate, based on your total income, while only taxing your Ohio income.
Ohio has a nonresident credit allocation form. IT NRC
https://tax.ohio.gov/static/forms/ohio_individual/individual/2022/itnrc.pdf
The credit is found on the “Schedule of Credits” and the calculation on the “Schedule of Credits” worksheet.
