If you did not pay the TurboTax account fees with a credit card prior to filing the federal and state tax returns, you will not be able to download a PDF of your tax returns until the IRS accepts the federal tax return on or after 02/12/2021.

When the PDF is available -

Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.

I did pay with a credit card, and still can't obtain a pdf version or print my state income tax submission.

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@eyebolt wrote:

I did pay with a credit card, and still can't obtain a pdf version or print my state income tax submission.

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What happens when you Click on Tax Tools on the left side of the online program screen.  Then click on Print Center.  Then click on Print, save or preview this year's return.  The select both the 2020 Federal and 2020 State returns and choose Include government and TurboTax worksheets