Is turbo tax going to file my school tax form?

What state?

If Ohio, 

TurboTax (TT) does not automatically prepare a School District return (form SD 100), you must initiate it.

At the screen, in the Ohio program, titled  "A few things before we wrap up your state taxes"
      scroll down to School District taxes. 
Or later at the screen  "Your 2023 Ohio Taxes are ready for us to check"
    -Click Other situations
    -Scroll down to School District taxes.

Usually  the School District Income Tax (SDIT) return  is e-filed with the state return, but there are exceptions. Read the Ohio 'filing instructions" that TurboTax prepares, They will tell you if the SD 100 was e-filed or if you have to mail it.