To  find out if you live in a school district or city with an income tax enter your address at:

http://www.tax.ohio.gov/Individual/LocalTaxInformation.aspx

 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. 

There are 2 state wide agencies that help Ohio Cities collect City Income taxes. One is CCA (Central Collection Agency) and the other, larger one, is RITA (Regional Income Tax Agency). There is a pull down list of cities, in Turbo Tax(TT), for both City Tax Forms (CCA) & RITA. But many  Ohio cities use neither agency. These cities design their own forms and require you to use them.  You can get paper copies from the individual city. Most are available at the city’s web site. Many cities will prepare the tax return for you, but you have to go to city hall in person. Some may have on line filing (try the city web site). Although they won't usually admit it, some will even accept CCA forms. So you could try filing out a CCA form on TurboTax and submitting it to your city; but I actually find it easier to fill out a city return by hand or at the city, CCA or RITA web site, than to use TT. Things don't happen automatically and you need to know what you’re doing. The actual  RITA/city forms are easier to follow than the TT interview.

For a list of all Ohio cities with an income tax go to http://www.tax.ohio.gov/municipalities/municipal_income_tax_forms.aspx

From there, there is a link to each city's web site including RITA & CCA