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Emergency services were called to an address at Barnett Ave in the Sydenham area of the city just before 3pm on Tuesday.
Six police cars, a fire truck and two ambulances are at a group of housing units owned by Otautahi Community Housing Trust.
St John referred all media enquiries to police.
A police spokeswoman said: "Police are currently attending a Barnett Ave address following a report of a sudden death.
"The death is currently being treated as unexplained, and inquiries are underway."
It comes less than a fortnight after Kenneth Daniel Hawkins, 50, was allegedly stabbed to death at the community housing complex where he lived in Sydenham.
A homicide probe was launched and a 28-year-old man has been arrested and charged with murdering Hawkins.