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.
Your return's electronic filing status history records all e-filing activity related to the return, including the Electronic Postmark. You can print it out if needed.
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp -- enter the Social Security number of the first taxpayer on the return and the ZIP code to retrieve your filing status history.
TurboTax CD/Download software
(Windows) From the TurboTax File menu, select Electronic Filing > Show Electronic Filing Status History.
(Mac) From the TurboTax File menu, select Check E-Filing Status.