A new mum was tailed by an Auckland City Hospital contractor as she carried her newborn son to her car and prevented her from driving away - with police having to intervene.

The mum - who gave birth 18 days ago at the hospital - claims the woman believed the baby was not hers. But police said they were called by "members of the public" after witnessing the woman "appearing to be having difficulty holding a newborn baby".

The woman - who is an older mum - told the Herald on Sunday she feared for her and her tiny baby's safety when she was approached by a woman on Thursday afternoon as she started to put her child in her vehicle parked in the nearby Auckland Domain.

She said the woman who police confirmed to her was a hospital contractor followed her about 1km on foot from the nearby wards of the central city hospital. She had attended an appointment to have her infant weighed and to thank surgeons for assisting in the recent delivery.

After feeding her baby she said the woman approached her as she prepared to strap her boy in his rear car seat, and insisted on holding the child.

The mum said the woman repeatedly made a beeline for his side of the car where the newborn was fastened whenever she tried to walk around to the driver's seat, stopping her from reversing out of her park.

"She kept asking over and over, 'Can I hold your baby? Can I help you? Can I hold your baby?'

"I said no. There was no way I was going to give her my child. Then she kept circling around my car.

"She was going to take the baby out of the car seat and take him," she said.

The mother became increasingly distraught. She was also desperate to leave because she had to collect a family member from school.

She said the woman refused to identify herself, concealing a hospital identity tag on her body. Police later confirmed to her that the woman was a hospital contractor.

While the drama was unfolding, the woman said she was sending messages to doctors she had just visited asking them to call her urgently, telling them she had been stopped for "abducting" her own child.

The mum, who did not want to be identified, said the standoff continued for at least 30 minutes.

"She said I should have been in a wheelchair and that the infant should have been carried in a car seat," she said.

As well as police being called, additional security staff from the hospital went to the scene.

After checking with the hospital, police confirmed the woman had given birth to the child in October and was able to leave.

She had also learned the police had contacted Oranga Tamariki who in turn contacted her midwife to see if she was fit to care for her child.

The mum claims in a later communication from police she was told "this woman had a perfectly legitimate reason to call the police because she thought something was out of place. She thought you were too old to have a baby."

The woman - who did not want to give her age - said she was "having no difficulty whatsoever" carrying her baby.

"He weighs only 3.1kg.

She now plans to carry her child's birth certificate in case another similar issue arises.

The woman said she filed a complaint with the police over the level of harassment she claims she experienced by the hospital contractor.

She was also to lay a complaint with Auckland City Hospital about the incident.

A police spokesperson confirmed officers attended the incident after being told by "members of the public" that they had "observed a woman appearing to be having difficulty holding a newborn baby".

"A hospital contractor has followed the woman out of the hospital grounds and into the Auckland Domain, and challenged her. A verbal altercation has taken place," the spokesperson said.

"Police arrived a short time later and all parties were spoken to. It was revealed that the woman was the mother of the baby and there was no further action required.

"Police continue to encourage members of our community to report suspicious behaviour. While in some situations, such as this one, we find there is nothing sinister, we still want people to report anything to police they believe is suspicious."

In a statement, the Auckland District Health Board said it understood the incident "will have been unpleasant for the mother and our clinical team is making contact to offer support".

"We take the safety of our staff, contractors, patients and whānau on our sites extremely seriously. We encourage any of our staff, contractors, patients and whānau who are concerned about the safety or behaviour of anyone on our sites to alert security immediately so security can respond as required."

It added that because the member of staff is employed as a contractor it couldn't comment further.

"We are in communication with the contractor about the occurrence."