When you called the state tax agency, did the state say they had received the tax return you filed? If so, had they finished processing and sent the refund? Or were they unable to find any evidence of your return having been filed?
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. Which of these terms is used there for the status--does it say accepted, rejected, printed, started, ready to mail, or what?
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.