It depends. Ohio does not tax the income you earn in Texas, but the income is factored in to calculate your overall tax.
Ohio does not have a true part-year or nonresident form, so for part-year and non-residents, all of the income is calculated as taxable in Ohio, applying any deductions and credits allowable against all of the income, and then a credit is applied back to the nonresident portion of income (income earned outside of the state is not taxed). The net result is the Ohio tax liability.
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