No.
Your state tax due cannot be paid from your federal refund.
It is not possible to pay your state tax due from your federal refund, nor is it possible to pay a federal tax due from a state refund. The federal and state treasuries are completely separate from each other. You may have seen a TurboTax summary of your federal and state amounts that confused you into thinking one was “paying” the other. It is not. The ONLY thing you can pay for from a federal refund is your TurboTax fees if you chose that option.
You must pay your state tax due using the state’s preferred method of receiving payment. For most states that will be by making a payment to the state’s own tax website, or by mailing a check or money order.
https://ttlc.intuit.com/questions/1900884-what-are-my-options-for-getting-my-state-refund-or-for-paying-any-state-taxes-i-owe
https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue