If you are filing because you have sources of income from Ohio (such as a rental income) and you still have ties to Ohio such as voter registration or a driver's license, file your return as a resident and list the county and school district where you last resided.
If you do not still have these ties, file as a nonresident and select any item from the drop-down box except for one of these states: I*ndiana, Kentucky, West Virginia, Michigan or Pennsylvania. Aside from these states, the selection will not affect your return (and is just a TurboTax interview question.)
If you do not have any income from sources within Ohio, Ohio does not require you to file to report income earned outside of the United States. However, if it is the first year that you have resided outside of Ohio it is recommended to file this return (by mail) with the state: Ohio Statement of Nonresidency. You have until October 15, 2020 to file the statement of nonresidency.
Ohio, unlike some forms, doesn't have a separate form for nonresident tax but simply adds a credit schedule to the tax return for nonresidents who are claiming credits for taxes paid to other states. In your case, this won't apply which is why the selection of a state will not affect the return (as long as you do not select one of the above-listed states with which Ohio has reciprocity.)
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