One way to verify is, 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.
You can also check your e-file status, please see the TurboTax FAQ below:
How do I check my e-file status?