Did you efile? Was your state return Accepted? Or did you print and mail it? Double check your efile status here
When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc. what does it say?
Check for a state refund https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
Make sure you are using the refund amount from your actual state tax return and not the combined amount Turbo Tax showed you at the end. That was for federal and state combined.
Contact your state
I used efile and my state refund was accepted. And when I track it it says that they we unable to locate my tax return using the info that I have given where in fact the details is correct.