Once your return is filed then Turbo Tax is done with it. You need to ask the state.
Did you efile? Was your return Accepted? Double check your efile status here
https://turbotax.intuit.com/tax-tools/efile-status-lookup
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?
To track your 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.
