Broughton had 12 days earlier struck Miss Aim's friend and workmate Zara Schofield several times with a rock, inflicting serious brain injuries.
He was in a pattern of nocturnal roaming - using alcohol and cannabis before committing the acts, for which he was sentenced to a minimum non-parole jail term of 12 years, making him one of New Zealand's youngest criminals to receive a life sentence.
Taupo CIB detective sergeant Anthony Manunui, who was second in charge of the investigation, yesterday could not tell Coroner Dr Wallace Bain whether Broughton was under the influence of drugs and alcohol.
"The reason I ask, of course, is that no rational, normal person could possibly have done that to Karen Aim, you would think, without being away with the fairies on something," Dr Bain said.
Mr Manunui replied: "I don't know whether he was on drugs prior to that incident ... I'm not sure what he was thinking during that incident."
He could not confirm whether Broughton had killed Miss Aim for money and drugs, as the boy's aunt earlier told Mr Aim.
Dr Bain said he had seen other cases involving unsupervised youth in Taupo, but Mr Manunui said he did not feel Taupo was "any worse or any better than a lot of towns in that respect".
After the inquest, Mr Manunui told the Herald the murder was one of the worst cases the town had seen.
"It certainly was difficult and with a tourist here in Taupo ... the circumstances were horrible."
But a family representative said Miss Aim's parents did not hold any grudge against Taupo or New Zealand.
"They've lost their only daughter and it's going to affect them for the rest of their lives, but it's their strong Christian faith which is getting them through, and they're all trying to get on with their lives," he said.
"They would have liked to know what the motive was - but I don't think they are going to find that out."
Dr Bain said the murder was shocking and blamed a lack of parental supervision. He will release his findings next month.
