I need to file state taxes for 2016 or file an extension because I owe,

If your federal return has been accepted you can e-file your state return.  E-filing a state by itself is only allowed once a federal return is accepted. 

To access your state return(s), after filing your federal return, please follow these steps: 

1. On the Overview page, click on My TurboTax > My Tax Timeline.  [See Screenshot #1, below.]
2. Click on Continue my [state] return.  [Screenshot #2]
3. If you have not completed your state return, click on the State Taxes tab.  If you have completed your state return, click on the Review tab and go through the prompts to file your state return.  [Screenshot #3]