Yes, if you are required to file school district taxes, you should see that information while going through the state portion of the TurboTax interview. And it will file with your return; unless it specifically tells you that you need to print and mail it. R.I.T.A. is one that has to be mailed. But the filing instructions will let you know.
If you have questions on school district taxes if you don't see it in your state interview, you can contact your state or city's Department of Revenue. You can go here How do I contact my state Department of Revenue? and select your state for contact information for department of revenue where you live.