On your RITA tax return, you can list your own locality or check to see if there is a 'out of state' code. This answer assumes you are filing your resident state locality return for your annual wages regardless of where earned.
Per the RITA FAQs page for Non Ohio Income:
Local taxes paid to a municipality outside the State of Ohio will receive the same credit allowed by your resident municipality for tax paid to municipalities inside the State of Ohio.
Generally, a county tax is not considered a municipal income tax and most municipalities do not allow credit for county taxes paid. Exceptions to this rule exist. For more information, visit the RITA Municipalities page, click on your municipality and review the Special Notes section that relates to the appropriate tax year.
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