First -- verify that your return has been filed and accepted --  then check the state web site to see where you are in the process-

Check Your E-File Status on this Secure TurboTax website
https://turbotax.intuit.com/efile/efile_status_lookup.jsp
- It will show the date you transmitted your return and if it was accepted or rejected.  
- Both your Federal and State will be listed separately if you filed both.
- It will tell you when you E-filed
- The electronic filing date

See the following TurboTax support article on checking your e-file status - https://ttlc.intuit.com/questions/1908859-how-do-i-look-up-the-status-of-my-e-filed-return

For the states:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
https://ttlc.intuit.com/questions/1901670-how-do-i-contact-my-state-department-of-revenue