Reports suggested a child had died at the complex on Barrington St in Spreydon on Wednesday afternoon, although police would not confirm the age of the person who died.
A child's scooter could be seen outside the home.
A neighbour, who did not want to be named, told RNZ she saw emergency services in the area, but did not hear a commotion.
"Our other flatmate came back home from work and said that there were heaps of ambulances and cops across the road," she said.
"There was a guy standing, like facing towards the fence with his hands above his head and the cop standing behind him.
"Our other flatmate was speaking to a neighbour and they said that there were heaps of ambulances, cops, fire trucks.
"They also mentioned that there were heaps of like, little kids on scooters around the area."
The woman said she would be distressed to learn that a child had died.
"That makes me feel sick to the stomach," she said.
On Thursday morning, police said they were treating the death as unexplained.
"Police are continuing to make enquiries into a death at an address on Barrington Street yesterday," they said.
"At this time, the death is being treated as unexplained."
In a statement, Kāinga Ora regional director for Canterbury Liz Krause said the agency's thoughts were with the friends and whānau of the person who died.
"While this death is under police investigation, it would be inappropriate for us to comment further."
