It only appears that Ohio is taxing all your income.
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 XX (Other state postal abbreviation) in box 15 of your W-2 screen, with the XX amount in box 16.
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
Per the Ohio Department of Taxation, Ohio taxes income on all your income but allows credit for taxes paid to other states. To enter the taxes paid to another state follow these steps:
Enter residency status
Continue through interview until you get to the "Take a look at Ohio credits and taxes" screen, click start next to taxes on income in other states
click yes for "Did you pay state income taxes to Ohio and another state on the same income?"
Enter State that other taxes were paid at
Enter the income earned and taxes paid to other state while an Ohio resident that was taxed by both Ohio and other state