In order to file a motion for examination, must the State first file a petition?
Our local juvenile judge seems to be unwilling to entertain a motion for examination until a petition has been filed and a cause number has been assigned to the matter.
Any thoughts?

I agree with your judge. Without a pending cause he has no jurisdiction to hear a mental health question. All of the provisions in the Juvenile Justice Code are related to juvenile age children who are referred to the juvenile court for a covered offense. Otherwise the cause should go before the court designated to handle mental health committments.