I have never heard of anyone not getting into high school because of a criminal offense. In public high schools, admission is automatic and you don't have to "get in" if you are the right age and grade.
You are right to be concerned. This one of just 2 schools in your public school system that is allowed by law to practice selective admission and the competition among applicants is very intense. You need to hope that the confidentiality provided by law for adjudicating your theft case is sufficient to keep the school unaware of this event. Note that if the school finds out about the theft case, the school is entitled to consider that info. Your rights to confidentiality pertain only to the criminal justice system's obligation not to disclose the result of your case.
Failing confidentiality (from community grapevine, other competitor-applicants, or other disclosure other than the courts), you need to prepare for the possibility that the application/admission process will offer an opportunity (essay, interview, etc.) that will allow you to demonstrate an appropriate maturing attitude and rehabilitation based on this event.
An important point: if you are successful in achieving admission to this school, the new challenge becomes how to hang on to your admission. Violations of the criminal laws have consequences -- always have, always will. You need to develop the skills to weigh the consequences before you act on any impulses. Not much point in getting admitted if down the road you are going to get kicked out for stealing.
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