Others in the area said the family didn’t often stay at the holiday home but were rowdy when they did, playing loud music and riding motorcycles.
Lake Hāwea residents were questioning why police didn’t launch a homicide investigation until eight months after White died.
Detective Senior Sergeant Regan Boucher said police were following positive lines of inquiry.
“Police believe people in the community hold important information about Mrs White’s murder and we encourage those people to come forward.”
Residents told RNZ that the community was shocked and they wanted to know how it took so long to become a homicide inquiry.
But they said they still felt safe in their small community, made up of a mix of full-time residents and holiday homes.
Boucher said police this week returned to examine the Lake Hāwea property with scientists from the ESR but would not reveal further details about their investigation or what was found.
In March, police initiated inquiries and treated White’s death as unexplained, conducting a scene examination across the week that followed and speaking with several people who may have been in the area.
Since then, police said, they had been working to determine what occurred before White’s death and a homicide investigation began after their inquiries led them to believe she died in suspicious circumstances.