What state are you in? What city and/or school district do you live in? What city do you work in?
If Ohio, city income tax (CIT) and school district income tax (SDIT) are two different things. Your employer must withhold for the city you work in (there is no "election" for that). Your employer may or may not withhold for the city and/or SD your live in. You'll have to ask them if they will do that. You do not have to pay SDIT to a SD you work in (but do not live in).
If SDIT was withheld while you did not live in that SD, you'll have to claim a refund when you file the SDIT return. You'll indicate that you were a part year resident of the SD.
