Do you mean a state tax due or an amount you entered?
If you owed a tax due,
Your only proof of payment is your bank statement or credit card showing the payment coming out. Turbo Tax only passes your bank account number to the state for the state to take it out of your account. But most states do not let you pay by Direct Debit so you have to mail in a check or go directly to the state's website to pay.
And you can not have a state tax due deducted from a federal refund. Never. Federal and state are completely separate. Turbo Tax just shows you a screen at the end showing the Net amount of federal and state combined. But it is just for your own info.