State refunds can take a long time, especially in some states who are cracking down on ID theft.
When you log into your account, what is showing for the "return status" for the state return? Does it say accepted, rejected, started, incomplete, printed, or ready to mail?
If you efiled, does the state return status show up in this tool?
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If it was accepted, then here's how to track the state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund