After you file

The Federal refund and the State refund come from two different tax agencies, so they are unlikely to come at the same time.  Either one can be delayed.

For some states, it can take several weeks to get a state refund.  Some states are taking a long time to process returns this year due to increased security measures and fraud detection techniques.

If you efiled the state return, first double-check that it was efiled successfully and accepted.  Use this tool:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp

Then in the FAQ below, click on your state to get info on how to track your state refund and how to contact your state tax agency, if necessary.  There is also a link in the FAQ about particular states with known delays this year.

https://ttlc.intuit.com/replies/3300211