Hegarty said that Glen Innes police wanted to hear from anyone who had seen any suspicious goings-on at the school.
"Some witnesses are yet to be spoken to. Others have been interviewed."
A suspicious fire that ripped through classrooms, an art room and resource room at Glendowie Primary in January was also still an open case.
Churchill Park principal Liz Gunn said a lot of people had wondered whether the two fires were linked, although Hegarty said there was no evidence to confirm this.
Police are also investigating a break-in at St Ignatius School in neighbouring St Heliers, in which a school office computer was taken.