Processing times vary from state to state. Some states may take up to 90 days or longer to process the returns and issue refunds. If you have successfully filed and the returns show as accepted in TurboTax, you will need to check your state's website to track the status of your refund. They will provide the most up to date status for you there.
The state does not send any updates to TurboTax after they accept your return. Once they approve your refund, they will update the status with a deposit (or check mailed) date for you, on their website.
And you can use your State Department of Revenue's website to check
status of state tax refund. Choose your state here
How do I track my state refund? and it will give you steps to track the status.
As much as we would like to help, TurboTax does not distribute refunds, only the IRS or your state tax agency can legally do so.
NOTE: If you track status and it shows as "no record;" that just means they have not started processing your return. Until they start reviewing/processing it, there will be no record. Just keep an eye out on the status page for updates.