To make sure that your payment is indeed scheduled, you can always reach out to your state's department of revenue for reassurance. Here's how to do so: How do I contact my state Department of Revenue?
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Was your state return accepted? Better double check.
Then 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.