Processing times vary from state to state. If you have successfully filed and the return shows
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.
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.
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.