Any type of taxes owed can Never be paid from any type of tax refund, Federal or State.
If you have local taxes owed those taxes must be paid by you directly to the local tax authority.
Sorry they were not. You can not pay a tax due out of another refund. Your only proof is your bank or credit card statement showing it being paid. You can only have the Turbo Tax fees deducted from a Federal IRS Refund.
Form 37 (RITA) cannot be e-filed. It must be printed and mailed. The Ohio Filing instruction should have indicated that it needed to be printed and mailed.
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.