The team is focused on the people who smashed windows at Taupo-Nui-A-Tia College in the early hours of Thursday. Detective Senior Sergeant Greg Turner said the windows were most likely smashed with a weapon using considerable force.
Police have not ruled out the possibility that the same weapon may have been used to kill Ms Aim.
"The longer they [the vandals] stay quiet, the stronger suspicion grows that they were responsible," Mr Turner said yesterday.
"It was a very vicious attack."
Police have eliminated robbery as a motive - Ms Aim still had her cellphone and purse when she was found.
They also said yesterday's post-mortem had shown no signs of sexual assault.
Ms Aim's body is to be flown home this weekend. It is understood her family - father Brian, mother Peggy and younger brother Alan - will not come to New Zealand.
Mr Aim, a builder, said he had been to New Zealand and thought it was a beautiful place.
"I loved the place and so did Karen," he said.
Ms Aim was in New Zealand for a second time after falling in love with the country on her first visit in 2006.
She had travelled in Australia and Thailand and wrote on her Bebo site how much she loved New Zealand.
She had toured the South Island with an aunt, skydived, bungy-jumped and was working at Taupo's Lava Glass Blowing Studio at the time of her death, overseeing the operation of the studio's gallery and cafe.
Studio staff, some of whom were international visitors like Ms Aim, were shocked by the brutal killing.
Ms Aim's bubbly, vibrant nature made her the ideal candidate for the role she occupied, said studio co-owner Christine Robb.
"Although she didn't work with us for a long time, because of her fantastic work ethic she made a huge impact here. She was absolutely perfect."
Her outgoing personality made her "the sort of person you would want to hang around a lot", and she had become close to some of the other staff in the few months she had been there.
It was clear she was loving her time in New Zealand, and having plenty of fun outside work, Mrs Robb said.
She understood Ms Aim had planned to stay in New Zealand for about eight months.
The family in Scotland asked to be left alone to grieve in private.
But a friend said her small home town of Holm and its 450 residents were devastated.
"It's an absolute tremendous shock for everyone in the parish," he said.
Mr Aim has asked authorities in Taupo to organise a memorial service for his daughter's friends here. Her aunt from Palmerston North is expected to attend.
Last moments
* Shortly before 2am: Karen Aim leaves Element Bar.
* 2am: She enters the BP station and buys a pie.
* 2.04am: Leaves the BP station alone and begins the 15-minute walk home.
* 2.07am: High school alarm is activated.
* 2.23am: School security guard calls police to report smashed windows.
* 2.34am: Police combing area near school find Ms Aim barely conscious in a pool of blood.
