First, you need to be sure your state return was successfully filed. If you efiled, be sure your efiled state return was accepted. If you used Online TurboTax, you can check by looking at the Tax Home in your Online account. What term does it show for the state return: accepted, rejected, printed, started, ready to mail, or something else?
Or did you choose to file by mail instead? TurboTax does not mail it for you. If you chose that method, you have to print, sign, date, and mail it.
The FAQ below tells how to check on a state refund and has a link for your state. Then you'll see information for your state (which may include info on how long it takes in your state) and a link to go to your state's "Where's My Refund" tool. It may also have a link to your state's department of revenue, if needed.
Choose your state from the table in this FAQ:
FAQ: How do I track my state refund?