What are you filling out? Your RITA tax return or your city withholding form for work?
You say you don't work in your residence city. What you don't say is where you do work. So, it matters whether you work in a city with an income tax or not. It also matters whether the city you live in allows a credit (and how much) for tax paid to the work place city.
Some Ohio Cities have an income tax. 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. If you live in a city with an income tax, you are subject to that city's tax as well. The city you live in will usually allow a credit or partial credit for the withheld tax you paid to the work location city.
Employers are only required to withhold for the work city, although many will voluntarily withhold for the resident city as well. Employees of most big companies, in Ohio, seldom owe any city tax, at tax time (but they still have to file a city return), because the employer holds out exactly the right amount for both work and resident city, taking into account the credit.
