How can I view and print my state tax return from last year?

To access your tax returns (current or prior year) you will sign into the TurboTax website with the user ID you used to create the account - https://myturbotax.intuit.com/

Scroll down to the bottom of the screen and on the section Your tax returns & documents click on Show.  Click on the Year and Click on Download/print return (PDF)

That only downloads my federal tax return not my state tax return

Please call TurboTax Customer service.  Here is a link:  Turbo Tax Customer Service