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
To track your state refund, select the link for your state below. If you’re looking for your federal refund instead, the IRS can help you.
Important: To help establish your identity, many states will ask for the exact amount of your expected refund in whole dollars. You can find this by signing in to TurboTax, and it'll be on the first screen. If you're using the mobile app, you may need to scroll down to find your refund amount.