Anyone with information relating to the incident could contact police on 105, quoting file number 201126/3921.
A teenager earlier appeared in the Wellington Youth Court charged in relation to the incident.
The boy, who cannot be named due to his age, faces charges of possessing five ammunition rounds and a .22 rifle without lawful excuse.
He appeared in court again this morning supported by multiple family members and was remanded by Chief Youth Court Judge John Walker in the custody of Oranga Tamariki to reappear next week.
Details of the hearing cannot be reported due to automatic suppressions surrounding youth matters.
Wellington High School principal Dominic Killalea said on the day of the lockdown the situation was challenging and teachers and students responded "wonderfully".
"There were, of course, students trying to do exams and many of them may have been affected by the information being received this morning."
He said there was a derived grade process that could be used for students affected.