Did you efile? Was your state return Accepted? Or did you print and mail it? When you efile you get back 2 emails. The first email only confirms the transmission. The second email says if the IRS (or state) Accepted or Rejected your efile.
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
How do you know it was approved if you mailed it? Mailed returns don't get Accepted or Rejected. Does it show up on your state's website refund lookup? You will have to ask the state where they sent it.