Police are also looking at links between her death and other incidents in the city the same day.
Mr Jeurissen said police had an open mind about the inquiry but were looking at links between the vandalism at the school and the attack on Ms Aim.
"It was a frenzied attack at the school and the damage at the school was extensive and the timing when Karen was found are very close."
He said there had been other reports of violence in the city the same day and police were looking at links between the events.
Meanwhile, Ms Aim's father Brian Aim, 51, from Orkney in Scotland, revealed that he and his wife had been planning to visit Karen.
He last spoke to her on the phone at the end of December when he told her that her beloved dog, Lee, had died.
"She was very upset but said the one good thing was that we could now go out to visit her in New Zealand because before that we would never leave the dog behind.
"I just can't think of Karen being murdered. All I want is her home. I don't think I will believe it until I see her body.
"I will always remember her wide smile and her chuckle.
"Her personality lit up every room she walked into.
"In our minds, Karen and Lee are now together in heaven."
Mr Aim - who praised police working on the case - said Karen was an artist who was making extra money selling paintings at the gallery of the factory where she worked.
"When we last spoke she was so happy. She loved New Zealand."
- NZPA
