I am not familiar with NJ tax laws. However, if your parents have to file their federal return by mail they also have to mail their state return. Your parents do not have to amend their return. They did not file incorrect returns. They simply need to mail correct original returns. A state return cannot be e-filed unless the federal has been e-filed. And....not sure why you were filing federal and state returns with no income----what were you trying to do?
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