I am filing fed taxes with Turbotax but I do not need to file state taxes because I have already done so. How do I skip the state tax part?

Select File by Mail to bypass the state forms. Of course, you don't have to file by mail. Selecting this just allows you to bypass the e-file prompts. 

But it might charge you for a state return.  To not pay for state now you have to delete it.  How to delete the state,   

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-delete-my-state-return-in-turbotax-online/00/25895