The mother of an extremely malnourished 11-week-old girl who died from child abuse on New Year's Day says she was a "very good baby" who was so happy she didn't cry.

The 24-year-old Otahuhu woman - who was this week charged with failing to provide the necessities of life for baby Tahani Mahomed - told the Weekend Herald she and her husband were still grieving for their daughter.

"It's very painful for us and very upsetting," said Tabassum Mahomed.

Her baby died in Starship hospital on New Year's Day.

An autopsy found Tahani had a skull fracture, brain haemorrhaging and retinal haemorrhaging which ultimately led to her death.

Along with the recent injuries, Tahani had two other broken bones, soft tissue injury and she was so malnourished that she had not put on any weight since her birth nearly three months earlier.

Detective Senior Sergeant Dave Lynch, who is leading the homicide inquiry into Tahani's death, said yesterday that she had suffered on at least three previous occasions in her short life.

"Without any plausible explanation provided, the nature of the injuries are such that experts conclude they are the result of child abuse."

Mr Lynch said inquiries had established that Tahani's parents were her only caregivers until December 28 when she was rushed to hospital.

That meant her parents - who had stopped co-operating with police - were considered the main persons of interest in the homicide inquiry.

Tahani's mother said yesterday that she could not talk about what happened or the charge she is due to appear in court on next week.

She did say however that Tahani had been a "very good baby" and that both her daughters were such good children that they never cried.

"They are very happy and enjoyable."

The Muslim woman, who is on a student's visa, and her husband Azees moved to New Zealand about a year ago from South Africa.

They also have a 2-year-old daughter who has been in the custody of Child, Youth and Family since Tahani died.

Tabassum Mahomed said she had seen her oldest daughter about once a week since she had been taken away.

When asked how the little girl was coping, she replied: "She's too small and she can't stay without us."

Police say they are still investigating the circumstances surrounding Tahani's death and can't rule out the possibility of further charges being laid.