If your non-resident state is not a "piggyback" state, you can e-file it by going through the Review and File sections of TurboTax.
TurboTax won't re-submit your the federal and state returns that you already filed, but if the state allows it, you can submit the non-resident state by e-file.
By the way, in most cases, you should file your non-resident state return first. This allows you to take a credit for the tax you paid to the other state (if any).
If you still have questions, please respond back to this thread with more details, including the names of the states that you are filing.