To see if your state and federal returns were e-filed/accepted, you can check the e-file status by clicking here: Check your e-file status
TurboTax gets its information right from the taxing authority, so if the e-file status tool says your return has been e-filed, you can count on that.
Once your federal return is accepted, your information will show in the IRS Where’s My Refund? tool.
To track your state refund, please see the information in this article: How do I track my state refund?
[Edited | 4/8/2020 | 11:57am PDT]