If your state return shows as "Started," it will show that way until your federal return has been accepted by the IRS (not accepted by TurboTax). It can only be e-filed once federal is accepted.
So if your federal return has been accepted by IRS, you can log back into your account and file your state return.
You can use the instructions below to help you file the state return at that time. Click the blue link below for the version of TurboTax you used, to get instructions.