Be sure you had School District (SD) income tax withheld and not City income tax. What @MindyB says is correct about Ohio City income tax, It is not refundable. School District Income Tax (SDIT) is a little different. You do not pay SDIT just because you work in the confines of an SD. Only residents of an SD are required to pay SDIT.
Most employers know better than to withhold SDIT just because you worked in the district. I suspect your employer considered you college residence as being within the SD and withheld SDIT.
That's a mistake and you are entitled to a refund of that withholding. You residence, for tax purposes, is still your parent's residence in the other state. You will need to file an SDIT return (Form SD 100) and indicate that you were an SD non resident (out of state) person. TurboTax can prepare theSD100, but it will have to be mailed and you will have to pay for Ohio software even though you will not be filing an OH state return.
You may want to try filing the SD100 at the Ohio Dept. of Taxation (ODT) web site. Even though SDIT is separate from state tax, SDIT is administered by ODT.
https://tax.ohio.gov/
