An Invercargill family has been left traumatised after a complaint by a fellow airline passenger lead to suspicions they were human trafficking.

Dr Amanda Sommerfeldt and her husband Scott were travelling with their 11-year-old son, Liam, and 8-year-old adopted daughter, Megan, who is Chinese, when they were met by police on the tarmac at Invercargill Airport on September 9.

The family, originally from the United States, had flown to and from Auckland that day to renew their children's US passports.

Sommerfeldt understood a passenger on the return flight had raised concerns with Air New Zealand staff at Auckland Airport that Megan wasn't related to them, and wasn't part of the family. The captain of the flight informed police.

Sommerfeldt said the experience was traumatising and was critical of the way Air New Zealand handled the complaint. Airline staff could have talked to the family and checked their identification documents before involving police, she said. 

"My biggest concern is we were targeted because of how our daughter looked," Sommerfeldt said.

"That's very concerning to me because it makes me afraid to fly again with my family. It makes me feel that anytime we fly, our daughter's at risk and this could happen again. And what about other adopted families or mixed-race families?"

During the flight, Megan was talking to a girl in the row behind her. Nothing seemed amiss, Sommerfeldt said, apart from one moment where a flight attendant stopped at their row and stared. No one from the airline spoke to the family and they had no interaction with the complainant, she said.

An Air New Zealand spokeswoman said the airline provided training to crew in relation to human trafficking in keeping with industry standards.

"We would again like to apologise for the upset and distress caused to the customer and her family. Our staff and crew onboard endeavoured to handle this matter as discreetly and respectfully as possible."

In an apologetic letter to Sommerfeldt, an Air New Zealand representative said the airline was "not the appropriate authority to make determinations on matters such as this and we refer these via the appropriate avenues to look into concerns.

"The decision to have police authorities meet the aircraft is made by the captain and after being informed of the observations, the captain on this flight felt it necessary to inform the relevant authorities."

Sommerfeldt said the family was met by police as soon as they left the plane.

Police did not immediately make it obvious why they wanted to talk to the couple and she initially thought their house had burned down or someone had died. When police mentioned a concern had been raised about their children, Sommerfeldt thought they had been accused of abuse.

"I'm sitting there going 'it's 9.45pm at night, somebody's accused us of abusing our kids. We're going to lose our kids,'" she said.

After questioning them for about 10 minutes, police said they were free to go. A police spokeswoman confirmed police were called to Invercargill Airport on Monday, and said police attended, spoke to the passengers, and determined no further action was required.

Sommerfeldt said Megan was scared by the incident. On the drive back from the airport, the children had been asking what police would do if they thought Sommerfeldt and her husband were not their parents.

Air New Zealand did not proactively contact the family after police resolved the issue to check how they were and explain what had happened, Sommerfeldt said. She remained concerned by the airline's approach.

"Is their human trafficking or exploitation policy based purely on anyone can make a complaint at any time and the police show up? Is it that a child looking different from the adults they're travelling with is enough to involve the police?

"If that's the case, I would expect them to go back and review those policies, because that's just not appropriate in the 21st century...It's discriminatory."