Did you efile it? Was it accepted? You can check your efile status here <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/efile-status-lookup/">https://turbotax.intuit.com/tax-tools/efile-status-lookup/</a>
Check for a state refund <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund">https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund</a>
But was your efile Accepted? Or did you print and mail it?
Then only the state can tell you. Did you look it up on their website?
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.