Constable Anton Perham said a 9-year-old girl from Pembroke School was reportedly chased by a male wielding a vacuum-cleaner pipe along Robertson St on Monday morning.
"She was walking to school, and saw a man running behind her. She believed he was chasing her and ran into the school grounds."
Const Perham said police had conducted a door-to-door inquiry into the incident, but residents around Robertson St had not seen the incident.
He said it "was still a bit of a mystery" and police would like to hear from anyone who saw anything.