Senior Constable Rowan Williams said large words were found on the main building of the school as well as on its fence in silver spray paint saying "Terrace'. Police believed it occurred between 7.30pm on Wednesday and 7am on Thursday.
They received information someone wearing a hoodie was seen and heard running near the scene about 6am on Thursday.
School board of trustees chairwoman Ellen Middendorf said there was "extensive" damage to the school, nearby trees and on a nearby street.
"It’s really disappointing. It’s extremely rare, especially this much of it. We didn’t want to file for insurance or anything, so some volunteers helped to clean it off."
It follows a spate of similar incidents in the town last month, including a vulgar phrase tagged on an Alexandra property, graffiti on St Enoch’s Church and a car being vandalised with spray paint.
Police did not respond to a question about whether tagging had become a problem in the area.
