When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.
First, check your e-file status to see if your return was accepted:
<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>
If the IRS accepted it, what does it say here?
<a rel="nofollow" target="_blank" href="https://www.irs.gov/refunds">https://www.irs.gov/refunds</a> Or does your account say “Ready to Mail?”
The fee you paid TurboTax (TT) to prepare a state return was only for preparation. There is a separate fee to e-file a state return (except NY). The free federal e-file does not include state. Check the "State filing instructions" work sheet that TT prepared (on your list of forms and worksheets) to see if your state return was e-filed or if you need to print and mail it.
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund