Police have released the name of a man and woman who were found dead in a South Auckland house along with a critically-injured child.

Photo: RNZ / Matthew Theunissen

Sherine Nath, 32, was found dead in the bedroom of a house in Papatoetoe near her critically injured son on Monday morning.

Riki Nath, 34, was found deceased in the garage at the same house.

A neighbour, who did not want to be named, told RNZ on Tuesday they were shocked to see police cars arrive, as there appeared no signs of trouble the night before or on Monday morning. The neighbour said the family had a lovely Christmas and they saw them outside the day before.

The four-year-old boy remains in a critical condition in Auckland's Starship Hospital.

Businesses in the area have offered their support to the child and a vigil was held during a South Auckland community event on Tuesday. A local resident who did not wish to be named said the incident had shocked the community.

"It is so heartbreaking to know that our community has suffered such a tragedy," he said.

"Our thoughts and prayers are with the young child who lies in the care of Starship Hospital. We want to encourage our community to stick together and stay strong through these times."

The deaths have been referred to the coroner.