If you live in a state that collects School District taxes, TurboTax will cover the topic in your state return. Even if you don't owe School District taxes, you'll still need to indicate which district you live in if your state requires a district code.
You'll
usually be asked to enter the code after identifying the name of the county in which you reside, depending on which state return you're preparing. Often, you'll simply choose from a drop-down list in TurboTax (click image for example from Ohio's return)
Start, revisit, or start over your state return to review/provide this required information.