The state could not have been successfully efiled if the fed was not successfully efiled ... check your spam folder for the missing emails.
When you e-file your federal return you will receive two emails from TurboTax. The first one will say that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state return.
Does your TT account say that your return was accepted? Or does it say something else—like “rejected”, “printed” or “ready to mail?” If it does not say accepted then it was not filed unless you put it in an envelope yourself and mailed it.
TurboTax does not mail your tax return for you.
You can check your TurboTax filing status here:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
You can check the IRS Where's My Refund website:
https://www.irs.gov/Refunds
Check your state refund here:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
