State Acceptance

"Accepted" = Accepted for Processing only. You alone are responsible for ensuring your State taxes are paid. Payment can Never come out of your IRS refund - although TurboTax provides you with the net sum of refunds and amounts owed, as information only. If your State allows direct debit, TurboTax will pass along numbers you provide for bank (routing and account) - but tracking actual payment processing remains Your responsibility, as verified from Your bank records. 

Accepted  just means they accepted your return for processing.  Only you would know if the tax due got paid.  Your 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.  

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-for-paying-any-state-taxes-i-owe/00/25954