You sure can start your state return, if your federal has already been accepted.
Just so you are aware, if you're using the Federal Free Edition of TurboTax, there's an additional cost ($29.99) associated with filing a state.
But here's how you would go about filing you're state return through the TurboTax account used to file your federal return:
1. On the Overview page, click on My TurboTax > My Tax Timeline.
2. Click on Add a State under SOME THINGS YOU CAN DO (If you haven't yet started your state return. Otherwise, click on the orange button, Continue my [state] return.)
3. Once you have completed your state return, click on the Review tab and go through the prompts to file your state return.
All the best!