"Started" means the state return has NOT been filed. My answer below tells how to go back and efile a state return that says "started."
However, if you are getting a duplicate SSN error because it's trying to efile the Federal, too, see this FAQ, which has a workaround. If you're getting that error, you have to first "fool" the program by choosing to mail it and then for the Federal return choosing "I'm not ready to file." Then you should be able to choose to efile just the state return. See the instructions in this FAQ:
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