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There is no federal law in the U.S. that gives service animal trainers the right to access public schools with their trainees. Some, but not all, states have such rights for trainers. However, they would only apply to the public areas of a public school, such as the gymnasium during a basketball game where any member of the public is permitted to attend.
In order to take a trainee into private areas of the school, where the general public are not permitted, such as classrooms while school is in session, the trainer would need to get permission from the school administrator first.