Hi, community! I was wondering, can I file my Ohio school district taxes through Turbotax?

Yes. 

TurboTax (TT) does not automatically prepare a School District return, 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 2019 Ohio Taxes are ready for us to check"
    -Click Other situations
    -Scroll down to School District taxes.

Usually  the School District 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 SD100 was e-filed or if you have to mail it.

It is too late to e-file a 2019 tax return (Federal, state or School District). 

You may no longer de able to do that with online TT.  

At this point, you may actually find it easier to do an SDIT return by hand, than in TT.  For the form, see https://www.tax.ohio.gov/portals/0/forms/ohio_individual/individual/2016/SDIT_SD100_Bundle.pdf

Instructions begin at page 50 at http://www.tax.ohio.gov/portals/0/forms/ohio_individual/individual/2016/PIT_IT1040_Booklet.pdf