Yes, you can NOT get that money back from Dayton. If you were a full year resident of MI or IN; those state have provisions for claiming a credit or deduction. Some KY counties and cities will allow a credit, but not the state. There are some other states that do so too, such as MD & KS
Michigan will give you credit for that on the state return, but you have to attach a copy of the city return. So, even though the Ohio city does not require you to file a return, you have to file one to get the MI credit, even though there will be no tax due or refunded from the Ohio city.
Some (but not all) IN counties also allow a credit, or partial credit for tax paid to an OH city. That will come up in the IN state interview. A $2000 income deduction IN use to have was eliminated starting in the 2016 tax year)
