Mansfield, Ohio Municipal income tax

You don't say:

1. whether your employer is also withholding Perrysburg tax

2. whether the Mansfield tax is prorated just for the one day a month

3. whether your home city also has an income tax and whether your employer is withholding for that city too

4. what your employer said when you asked why they withheld Mansfield tax

5. How your employer is handling city taxes for the cities in the  four counties that you do work in

You may be  entitled to refund for days you did not work in Mansfield. You'll need to file a non-resident city return to get a refund. It's a good idea to contact the city first, because they may require a special form for this situation. TurboTax cannot do a Mansfield return. 

 But, if you happened to work those days in other cities that had a tax; you would then owe tax to those cities. You usually do not have to pay taxes to a city that you worked in 12 days or less (20 for RITA cities).

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.