A mother whose 3-day-old daughter died hours after a doctor prescribed paracetamol for flu and sent her home is demanding answers.

Westcare White Cross medical centre in Henderson has started an internal investigation into the care given to Patience Aroha-Tae Kahaki, and her death has been referred to the coroner.

The child was born two weeks prematurely on April 5 at Waitakere Hospital after her mother, Nicole Kahaki, was admitted because of bleeding and high blood pressure.

The Hamilton woman, who had been visiting family in West Auckland, left the hospital the day Patience was born.

But two days later, the baby became irritable, crying constantly and refusing to feed.

Ms Kahaki took her to the Westcare medical centre about midnight.

The 34-year-old, who has five other children, says a doctor there told her not to worry as Patience had a common case of flu.

The baby was given half a millilitre of paracetamol, saline was put up her nose to clear her airways, and she was sent home.

But about 45 minutes later, Patience went limp in her mother's arms.

"She started crying like a lamb again, she tilted her head back, eyes dilated, looked at me and that was it. I could see she was gone."

Ms Kahaki and a neighbour tried desperately to resuscitate the baby until ambulance officers arrived and took over.

Patience was taken to the emergency department at the Starship hospital but doctors were unable to save her.

Ms Kahaki believes that if the Westcare doctor had referred her to the hospital immediately, Patience would be alive today.

"I felt robbed. I'm not dealing with it well. It's not knowing that gets me. Every day goes by and there's nothing. It's like she never existed. Just gone back to normal, just had a baby, the baby's gone and there's nothing."

Ms Kahaki said notes from the Starship said her daughter had a heart murmur, but she was still awaiting autopsy results to confirm the cause of death.

She is considering complaining to the Health and Disability Commissioner about her daughter's care at the Westcare centre.

White Cross chief executive Alistair Sullivan said an internal investigation was being held into the child's care.

He was also awaiting the autopsy results to aid the investigation, and would not comment specifically on the care of Patience because of patient confidentiality.

A spokesman for the Auckland coroner's office, Malcolm Mott, said the unexpected death had been referred to coroner Dr Murray Jamieson, who was waiting for the pathologist's findings before deciding whether an inquest should be held.

It was not uncommon for post-mortem results to take weeks or even months, he said.

It was not the coroner's role to lay blame. He could make recommendations, such as suggesting an investigation be held into the way the medical centre handled the baby's care, but could not by law enforce them.