Get your taxes done using TurboTax

Of course you can do state returns.  After you enter your federal info you continue on by clicking the state tab on the left.  You do have to be in the same account that you did federal.  Click on Add a State to let you back into your return.  Where are you stuck? Are you using the Online version or the Desktop installed program?  There are a couple Desktop versions that don’t come with state but you can add state on.  

Did you already file federal?  you can only efile state if federal was first efiled and Accepted.
How to file state after federal

https://ttlc.intuit.com/community/e-file/help/how-do-i-e-file-my-state-after-i-already-filed-my-fede...