If it was not accepted then the state wouldn't know you owed.
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...
