Several key members of the Kahui family are maintaining their silence more than two weeks after twin babies Chris and Cru were murdered, possibly by violent shaking.
The 3-month-olds were taken to hospital on June 13 and died five days later from multiple injuries and severe brain damage.
Detective Senior Sergeant John Tims said yesterday the case was a double-murder inquiry, and the investigation was likely to continue for a number of weeks.
Police had interviewed a number of family members but the investigation team was "working through some key issues" around several people who were yet to talk.
They belong to the so-called "Tight 12" of family members who had contact with Chris and Cru before they died.
Mr Tims would not comment on the issues facing police. Family members have hired a number of lawyers and some have changed their legal representation during the investigation.
The twins' parents, Sonny Chris Kahui and Macsyne King, have been interviewed by police at least twice.
Mr Tims said he would not speak to media again until Monday unless there was a significant development in the case.
"The filming of the investigation team at work, confronting our witnesses, is not helpful to this inquiry," he said.
"This investigation cannot be rushed. I will not be rushed. It is unique on a number of levels."
Family spokeswoman Ani Hawke, a first cousin of Mr Kahui's mother, Gwen, said the doctor in charge of the twins told the family the injuries may have been caused by shaking.
"The incident was performed by somebody who, to put it into layman terms, if you liken it to a ping pong ball or a marble in a bottle and you shake it. When you stop shaking the bottle the marble or ball carries on. And that happened to the babies. They've been shaken and when they stopped the brain has kept on moving."
Mr Tims would not say if police had a main suspect or confirm a suggestion from Ms Hawke, that the family had been told by the hospital the injuries were probably caused by shaking.
"We are still waiting for our pathology evidence and I won't comment until I have that in writing. I won't comment on the injuries ... other than that Cru and Chris received multiple injuries, including brain damage."
He described the babies' injuries as at "the high end" of child abuse.
"This case is murder. It involves two twins, 3-months-old."
Chris and Cru were born premature at 29 weeks.
Counties Manukau District Health is making a mortality review, standard procedure when a child dies while still in hospital care.
The Kahui twins were being monitored by the hospital's extramural neo-natal service and were reported as healthy and well nourished in the week before they were taken to hospital with brain damage.
Ms Hawke disputed the police statement that several family members had not come forward for an interview. She said the 12 people in contact with the twins - including grandfather, William "Banjo" Kahui, aunt, Mona-Louise Kahui, and uncle, Stuart King - had spoken to police.
Mr Tims acknowledged he was heading a high profile inquiry and said police appreciated public support.
People were entitled to personal opinions about the case, "but I must deal with facts, evidence not emotion".
- additional reporting, NZPA
Key Kahui whanau still to be interviewed
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