"We would launch an investigation if we could but at this stage no one's come forward," she said.
A parent can be fined for leaving a child alone, but Senior Sergeant Justin Rakena of Porirua police said earlier today that if a formal complaint was made it was unlikely to result in criminal charges against the mother.
He said it was dangerous for parents to leave their children in the car, although in many cases there was an "innocent" explanation, and the best solution was support for the parents from Child, Youth and Family.
"[Incidences like this] need to be taken on their merits and often it's a mum that's run into a shop, for example, and is only away for five minutes," Mr Rakena said.
"Absolutely [it should be reported to police], but it doesn't mean to say we'd prosecute. I would suggest the majority of people in that situation aren't prosecuted."
The man who spotted the baby on Saturday when he and his family parked in the neighbouring space said he was shocked to see the hand-written note resting on the child's blanket.
"It was written from the baby's perspective, and it said, 'My mum's in doing the shopping, call her if I need anything', and it had the cellphone number.
"We waited there for a little bit, wondering if the mum was just going to be two seconds and come back. And my wife said, 'I'm not going in without someone being here with the baby'."
Eventually another two passers-by waited by the car, with one of them phoning the mother and telling her to come outside.
"We had gone in [to Pak'nSave] before the mother had come out because we had a baby ourselves that was in a hurry."
The man said the baby looked well cared for.
Plunket national child safety adviser Sue Campbell said the risks of leaving a baby or young child alone in a car were significant.
"Babies can dehydrate quickly and become very distressed. So for a newborn that's one of the key issues. Plus there's a security issue - a small baby is unable to defend itself if need be, or call for help, or anything like that."
Ms Campbell said the circumstances of the mother were not clear, and caring for a baby could be overwhelming, especially for those without ready family support.