No. Any Ohio
city, with an income tax, is allowed to have withholding taken out of your pay
while you worked in that city. Your employer is required to do that
withholding. You can't get a refund unless it was improperly withheld, i.e. you
didn't actually work there for all or part of the time that your employer was
withholding.
You normally only have to
file a return in the city you live in. It is not necessary to file one in the
city you work in, if different. Your employer will remit withholding to the
city you work in, but you do not file a return unless you're claiming a refund or your employer didn't
withhold enough ( both highly unusual). The city you live in will allow a
credit or partial credit for the withheld tax you paid to the work location
city.
If you don't live in a city with a tax, Dayton still gets to keep your money.
