Heather Foote, 56, died on July 28 - two days after she was found with critical injuries at her Port Hills Rd home in the Heathcote Valley area.
A post-mortem examination was carried out but the investigation into her death is ongoing.
Detective Senior Sergeant Craig Johnson said the death was still unexplained.
"We are working with family and friends of the deceased to better understand the circumstances surrounding her death," he said.
No one has been charged in relation to Foote's death and at this stage Johnson could not be drawn further on the specifics of the investigation.
A scene examination was carried out at the house where Foote lived with her children.
The mother-of-four was farewelled at a private service.
"Family and close friends would like to thank the community of Heathcote in particular, as well as the wider public for their humbling support, kindness and love freely shown towards Heather and her family," a public notice published after her funeral stated.
"Those that spent the last hours by Heather's side would like to thank the amazing medical teams at the hospital for their care of Heather and the compassion shown, both of which far exceeded their collective job descriptions.
"The family would also like to acknowledge and thank the police for their support and guidance for and to the family and close friends.
"A service has been held for Heather after which she popped in to see mum."
A Givealittle page has been set up to support her family.
"This page has been set up in response to requests from members of the community to enable people to offer their support for Heather's family at this tough time," it said.
"Heather's sudden passing has been a devastating loss to her children, three of whom lived with her full time.
"There are many unexpected financial costs that are adding additional burden at the moment. Any support that can be offered at this time will be greatly appreciated."
More than $2000 has been donated since the page was established.
Tributes have also been posted online for Foote, who worked at a local fireworks company until the effects of the Covid-19 pandemic hit New Zealand.
Colleagues described her as a "devoted" mother.
A friend thanked Foote for "the good times" and said she was "lovely".
"Queen of curries, wonky parking, foghorn volumes, and all the lols and love," she wrote.
