You have not mentioned what state you are asking about so we do not know what form you are trying to get.
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. Some states process returns quickly and some are very slow.
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
https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/0...
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**