Processing times vary from state to state. Some may take up to 90 days or more. 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. Accepted in TurboTax just means the government received it. That is the status of your return; not your refund.
The state do not send any updates to TurboTax after they accept your return. Once they process your return and 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.