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Te Kahika took to social media to confirm he was reluctant to use a mask to cover his nose during the flight.
He claimed that covering the nose "feels wrong".
During the flight he was challenged by a stewardess who told him he needed to wear the mask correctly.
The stewardess asked him three times to wear the mask properly and he refused.
When the flight landed in Dunedin a policeman and an Air NZ manager were there to meet him.
Te Kahika Jr said he challenged the stewardess, police and the Air NZ manager about the legal basis for wearing a mask, saying it was not in Covid-19 legislation.
The Covid-19 legislation does not refer to masks, but the Civil Aviation Act requires passengers comply with orders from the pilot-in-command.
Police said they could not comment on whether an individual was under investigation for privacy reasons.
Wearing masks is mandatory on public transport and flights in and out of Auckland while the city is in Level 2, though Air New Zealand has made them mandatory on all flights until the whole country is in Level 1.
The Ministry of Health says masks and face coverings can reduce the risk of people who have Covid-19 spreading the virus to others through infectious droplets.
The World Health Organisation says that while the prolonged use of medical masks can be uncomfortable, it does not lead to oxyen deficiency or CO2 intoxication. Masks should not be worn when exercising, the WHO says.