How did you elect to pay the state taxes owed?
Most states do not allow a direct debit from a bank account when using personal tax preparation software.
In the File section of the program when taxes are owed you are given specific instructions on how the state taxes owed can be paid.
Look at the State Filing Instructions page for how you selected to pay the state taxes.
TurboTax will only reimburse penalties and interest for a calculation error made by the software. See this TurboTax support FAQ - https://ttlc.intuit.com/community/charges-and-fees/help/how-do-i-submit-a-claim-under-the-turbotax-1...
