According to this (admittedly not exactly a SCOTUS ruling), it is permissible but there are boundaries.
http://wiki.answers.com/Q/Is_it_lega...hile_in_school
Quote:
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School officials can ask whatever they so choose, so can the police. However, a child, by law, can say, "I would like to have my parent present. Or, I would like to have an attorney present." At this time, by law, questioning should cease and desist.
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If this quote is true, then the cops violated the law by continuing to question the child once he said he was unwilling to talk with them.