TurboTax gets no information from the state after your return has been accepted for processing. TurboTax cannot track your refund or tell you why the state is not answering calls. You have to track your refund for yourself.
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/00/25573