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The permanent police presence at the facilities was introduced after a 32-year-old man absconded from the Stamford Plaza in Auckland's CBD for 70 minutes on Tuesday night.
He tested positive for Covid-19 the next morning.
Police have indicated they will charge the man.
It was the second time a person had fled from a facility in Auckland this week.
"We will come down on them with the full weight of the law," minister in charge of managed isolation facilities Megan Woods said yesterday.
"They are putting New Zealanders at risk.
"Frankly, they don't deserve to join the team of five million."
Three new Covid-19 cases were confirmed in New Zealand yesterday, all of them in isolation facilities.
Two of the people had travelled from India and one from Italy, and they were aged in their 20s and 30s.
In all, there are 24 active Covid-19 cases in New Zealand, and 5468 people in managed isolation or quarantine.
Head of managed isolation and quarantine Air Commodore Darryn Webb said a uniformed police officer would be on site at each isolation facility 24 hours a day, which would help ensure compliance.
Police Association president Chris Cahill told RNZ last evening the move had political elements, and was not the best use of police resources.
He said there was certainly an element of a feel-good factor, and it was a distinct possibility that it would mean the public was less safe than otherwise.
"Is that the best priority? To feel good, if it doesn’t actually have a dramatic change in the security of those facilities? ... I don’t believe it does.
"I think there’s a degree of making it look that politicians are doing the utmost they can — and I understand that, and New Zealanders want the utmost to be done — but I don’t believe that requires 24/7 police presence."
Mr Cahill said to fully staff and monitor the facilities would take between 150 and 200 police officers who were needed in the community.
"We’ve got police districts that don’t have many more than 200, 250 sworn staff, some of our smaller police districts, so it’s a significant number.
"It’s certainly not a core policing role."
"This is a job that can be done by aviation security staff, customs staff, immigration staff — the people that aren’t fully utilised due to Covid issues that are created at the border," Mr Cahill said.
He said director-general of health Ashley Bloomfield could give those staff the powers they needed to do the job just as effectively as police.
There were already 400 Defence Force troops stationed at the facilities and, he argued, there was not much need to have police there as well.
"If there was clear evidence that police powers were required regularly because people were trying to break the quarantine rules that would be understandable, but there’s no evidence supporting that.
"Policing can be called in when there is a significant issue of someone not following the rules, but we’ve only seen two people that appear to have breached those rules, so it’s not an issue of having all these officers standing around waiting for that ...
"I think you have to be realistic. Two runners out of thousands of people that have gone into quarantine is not a great number and my information is only one of those was deliberate, one of them was ignorance."
Mr Cahill said he had spoken to police commissioner Andrew Coster about the matter, and hoped to speak to Dr Woods today.
— RNZ/The New Zealand Herald