You can NOT get the OH local (city) tax refunded*. The OH-IN reciprocity agreement does not apply to local city taxes. You are not required to file a local city return, but you are also not entitled to a refund of the city withholding (box19 on your W-2), unless there was an error in the amount.
Most IN counties (but not the state) allow a credit, or partial credit for tax paid to an OH city. That will come up in the IN state interview. (For details, see:
https://ttlc.intuit.com/community/state-taxes/discussion/i-see-no-separate-question-for-school-taxes...
*In the unlikely event that Ohio School District tax was withheld, rather than city tax, you can get that refunded.
