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
TurboTax does not receive updates from your state once they have accepted your return. You will need to obtain that information directly from your state office as each state has different timing for processing tax refunds. The refunds are processed separately by different agencies and the timing is independent of each other. The IRS processes federal refunds and your state Department of Revenue processes the state tax return refunds. It is not unusual that one arrives before the other. Please see this TurboTax FAQ for your Department of Revenue contact and refund information: https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/00/25573