It depends.
If the status of you state tax returns show they have been accepted on the TurboTax software, then they have been filed and accepted by the state. TurboTax no longer has any control over the tax returns after they have been accepted.
You will need to follow up with the state. Attached is a link to the state websites. Click on your applicable state to follow up with them directly.
How to track my refund
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