Only the state tax agency will know what all they are doing with your return. Many states have had delays this year as they crack down on fraudulent returns. But we can tell you some things to check.
First, you need to be sure the state return was actually filed. How did you file the state return? Did you efile, or did you choose to print, sign, and mail?
When you log back into your account, what do you see for the return status for the state return?
If you efiled, double-check with this tool to be sure the state return was efiled successfully and accepted:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp Or if you filed by mail, did you print, sign, and mail it? TurboTax does not mail it for you.
The following FAQ tells how to track a state refund and how to contact your state department of revenue, if necessary.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/replies/3300211