Anyone refusing to obey a quarantine order can be forcibly detained or fined $2000, but such orders are unlikely unless a person suspected of endangering public health is dobbed in to health authorities.
The Government can also order a foreigner with Covid-19 to be deported, but there is no specific clause in the Immigration Act to do so for public health reasons, which could invite appeal or challenge by judicial review.
Concerns over whether people will flout self-isolation - potentially endangering the health of others - have soared since strict travel restrictions came into effect this morning.
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The restrictions, which are expected to swell the number of people self-isolating, mean that anyone coming to New Zealand from anywhere but the Pacific will be asked to self-isolate for 14 days.
Prime Minister Jacinda Ardern has moved to allay concerns, saying about 10,500 people had self-isolated so far and had been overly compliant, with some staying at home for longer than 14 days to be on the safe side.
But she said police could force non-compliant people into quarantine at a medical facility, with staff stationed at the door to ensure no one escaped.
This power had yet to be used, she added.
This morning she added that she would look into the Government's ability to deport travelers who refused to self-isolate.
Last week Covid-19 was designated as an infectious disease and a quarantinable disease under the 1956 Health Act.
That means that entire ships or airplanes - and everyone on board - can be quarantined, and anyone thwarting this could face three months' jail or a $2000 fine - or both.
A different order can be imposed on an individual to prevent them from doing a specific task - like taking the bus - being in a specific place, or associating with specific people.
Such orders can be made by a medical officer of health, essentially a public health doctor who his accountable to the Director-General of Health.
But these orders are not made proactively, meaning that an officer is normally alerted to a suspicious person before an order is considered.
"It will have to come from a whole variety of third parties," said Louise Delaney, a public health lawyer at Otago University.
"It might be their health practitioners or family or friends, people who are worried that this person is going out and maybe sick but doesn't know it."
Failure to comply could see a $2000 fine, but Delany said a stronger option was available - a public health order.
Such an order, which has to be signed off by a District Court, could see someone forcibly detained in a medical facility. Failure to comply carries a penalty of six months' jail or a $2000 fine.
Delany said these orders had only ever been used twice since the law was passed in 1956.
"They were real detention powers. They were locked up. We've only used them twice and both times for people with HIV."
"Special powers" are also available to a medical officer of health, but they had to be signed off by the Health Minister, unless a civil defence emergency or epidemic had been declared.
Delany was not aware if special powers had ever been used, though they were considered during the global SARS outbreak.
"This is all uncharted territory," Delany said.
"What we're really facing here is quite unprecedented."
Delany said there was nothing in the Health Act that allowed deportation for public health reasons.
But under the Immigration Act, the Immigration Minister could deport someone on a visitor visa if there was "sufficient reason".
But that could be appealed, which could delay any action for two to three months, according to Simon Laurent, an immigration lawyer and a director of the NZ Association of Migration and Investment.
A deportation order could also be made through Order in Council for "security" reasons, for which there was no right of appeal - but it could be challenged by judicial review.
Such a challenge might succeed by arguing that public health was never intended as a threat to "security" when the law was passed.
The Government could look to pass an amendment under urgency stating that public health reasons - specifically related to Covid-19 - could justify deportation.
There is no indication that this is being looked at.
National's immigration spokesman Michael Woodhouse said he couldn't speak for the caucus, but he personally might "look favourably" on such a proposal to protect against the spread of Covid-19.