You have not mentioned which state. There are states that are not yet accepting e-files. And....it usually takes a day or two after the IRS accepts your federal return before the state accepts your return, so keep watching your emails.
When you e-file your return you will get two emails from TurboTax. The first one will say your return has been transmitted; the second one will tell you the IRS has accepted or rejected your federal e-file. If you filed a state return, there will be a third email (usually a day or two later) that tells you if the state e-file was accepted or rejected.
Check your e-file status:
https://turbotax.intuit.com/tax-tools/efile-status-lookup/