You must file in both states. You file as a non-resident in Utah because the unemployment is derived from work you actually performed in Utah. And you file in Ohio because Ohio taxes all the income of its residents, regardless of the income's source.
Ohio will give you a credit for the taxes you pay to Utah on the dollars that are taxed by both states, so in effect you won't be double-taxed.
With TurboTax, complete the non-resident tax return before the home state tax return, so that the program can calculate and apply the credit.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
