No, you do not have to pay taxes in Ohio, but you must file a non-resident tax return to get a refund. Once you complete your federal tax return, move to the state section where you will see the non-resident tax return for Ohio and the resident tax return for Washington. Make sure that you prepare your non-resident tax return first for Ohio. You should get a refund of the taxes withheld from your paycheck. When you complete your resident tax return for Washington, you may owe if your employer did not withhold taxes for Washington.
Please review the TurboTax Help article How do I file a nonresident state return? for additional information. You can also review Employer Withholding #8 on the Ohio Department of Taxation website which outlines employer’s responsibilities regarding withholding for employees who live and work in another state. You can also complete Ohio Form IT 4 Employee's Withholding Exemption Certificate (check you are exempt from Ohio withholding under R.C. 5747.06(A)(1) through (6)) and provide to your Payroll Department so they will stop withholding taxes from your paycheck.
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