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

https://ttlc.intuit.com/community/state-taxes/help/how-do-i-contact-my-state-department-of-revenue/0...

Did you e-file your tax return and was it accepted?

Only the IRS and your State control when and if a Federal or State tax refund is Approved and Issued.

You complete your tax return by finishing all 3 Steps in the File section. In Step 3, to e-file your tax return, you must click on the large Orange button labeled "Transmit my returns now".

After completing the File section and e-filing your tax return you will receive two emails from TurboTax. The first email when your tax return was transmitted and the second email when the tax return has either been accepted or rejected.

To check the status of an e-filed return, open up your desktop product or log into your TurboTax Online Account. You can find your status within the TurboTax product.

If accepted by the state use this TurboTax support FAQ to check the state tax refund status - https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund