Your proof of payment to the state is the cancelled check, bank or credit card statement showing the payment.

How you chose to pay the state taxes owed will be on the State Filing Instructions page included with your tax return.

Sign onto your TurboTax online account - https://myturbotax.intuit.com/

Scroll down and click on Add a State.  This will take you back to the 2019 online tax return.

Click on Tax Tools on the left side of the online program screen. Then click on Print Center. Then click on Print, save or preview this year's return.

TT doesn't pay the state  and it cannot be paid with a federal refund.  If you paid the state then your proof of payment is the CC charge or cancelled check or  debit on your bank statement. 

To access your current or prior year online tax returns sign onto the TurboTax website with the userID you used to create the account - https://myturbotax.intuit.com/

When you sign onto your online account and land on the Tax Home web page, scroll down and click on Add a state. 

This will take you back to the 2019 online tax return.

Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.  Choose the option Include government and TurboTax worksheets

For the State taxes owed  the bank name, routing number, account number and the date you selected to pay the taxes owed will be entered   will be on the State Information Worksheet in Part V of the worksheet and on the State Filing Instructions page.

However most states, if not all, do not allow state taxes owed to be paid by Direct Debit when using tax preparation software.  They require the payment by Direct Debit only when using the State tax authorities website.

How did you pay the state tax due?    Your only proof is your bank account statement or credit card statement showing the payment coming out. And Turbo Tax doesn't pay any tax due for you. Turbo Tax just sends your payment method to the state. You either put down your bank account number for the state to pull it directly out of your account or you needed to mail in a check. Most states don't let you pay by direct debit. Did you check your bank account to see if it came out? You should have an instruction sheet telling you how to pay it.

Oh, and you can't have a state tax due deducted from your federal refund. Never. You can only have the Turbo Tax fees deducted from your refund.
https://ttlc.intuit.com/community/state-taxes/help/can-i-pay-my-state-taxes-from-my-federal-refund/0...

Check the printout or PDF of your return; look for the state cover sheet with the Turbotax logo. If you owed tax, it will show the payment information and how/when you decided to pay. Read the state payment instructions carefully since most states cannot be paid from within the TT system and requires additional steps.
https://ttlc.intuit.com/community/refunds/help/what-are-my-options-for-getting-my-state-refund-or-fo...