Federal and state refunds come from completely separate entities,  There is no rule as to which one will come first or how much time there will be between their arrivals.

STATE RETURN

Make sure your state return was accepted:  https://turbotax.intuit.com/tax-tools/efile-status-lookup/

To track your state refund:    

https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund

Does it say Ready to Mail?  

Did you efile?  Was your state return Accepted?  Double check your efile status here

https://turbotax.intuit.com/tax-tools/efile-status-lookup  

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?