In the second incident, which can be revealed today, students visited the local Pak'nSave, on the same street, with one girl wearing a swimsuit.
Principal of the $20,000-a-year school, Lynda Reid, denied rumours the student was topless, and said another allegation involving a student being tied to a poll on Eruera St was untrue.
"We can confirm that no student ran topless through Pak'nSave. She was wearing swimwear and was covered appropriately with a towel. To our knowledge, the pole event did not happen with our students."
Rotorua Bike Barn employee Ruthy Arrowsmith, who witnessed the stripping incident in front of her work place, said she spoke to three adults (a man and two women), who appeared to be the student's supervisors.
"They told me it was like an initiation, something like the Amazing Race. They all seemed to be bragging about it, one lady even told me that the girls had run through a supermarket earlier, carrying a towel, screaming for shampoo, naked," she said.
A Pak'nSave supervisor said they were unaware of the allegations.
Ms Reid said the school was taking the stripping incident "very seriously" and would be "conducting a thorough investigation".
"The coach who was with the students was not an employee of our school but a professional working on a paid external contract. The coach has been stood down while the investigation is conducted.
"As a school we are viewing this incident very seriously and I apologise to the people who were upset by the student's behaviour however, we must remember this was the behaviour of a young student who did not consider the consequences of her actions.
Organisers of the tournament, New Zealand Secondary Schools Football, confirmed it would be looking into the incident.
"We wouldn't condone any behaviour like that," Leigh Perry, national administrator, said.
An executive committee, which has representatives from the school involved, will be involved in the "wash-up" once all the information had been collected, she said.
"The school are responsible for the discipline of their own students.
"We will deal with that [incident] with the school concerned."
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- Additional reporting by Teuila Fuatai of the New Zealand Herald