It said a private funeral would be held with a memorial service at a later date.
Earlier, RNZ spoke to neighbours on Baroda St who said the mood in the area was eerie and sad and they were trying to come to grips with the homicide investigation.
One neighbour, who did not want to be identified, said Gregory - who had gone to school with their aunty - spent a lot of her time gardening.
They said she was very old school and people would have mixed opinions about her - she either liked you, or she did not.
The amount of gardening she did and the layout and size of her hilly property helped keep her fit and out of a retirement home, they said.
The neighbour said Gregory’s only visitors were her daughter or, as she got older, her gardener.
Steve Watt said residents on Baroda St were anxious for answers in the next few days.
“It’s pretty sad really to know that someone in your own street and neighbour, especially an older lady living on her own, that that’s happened you know to someone like that, especially in a quiet little street like this. But I suppose there’s a few concerned residents but they just want to know what the full story is.”
Watt has lived on Baroda St for 20 years and said during his time there he only saw Gregory a handful of times. He said she was a quiet lady who kept to herself.
Police did not think there was ongoing risk to the public, and anyone with information should contact them.