A police spokeswoman said inquiries into this incident were continuing and police would not make any further comment at this time.
A spokeswoman from the NZ Racing Board said the agent which operates the Pāpāmoa TAB branch was assisting police with their inquiries.
"We are unable to provide any further details about this matter as this is an ongoing investigation," she said.
Fashion Island centre manager Roz Irwin said the TAB branch was situated on land not owned by the shopping complex but she dealt with a similar incident a few weeks ago.
"Just before Christmas a child aged under 2 was left strapped into a car seat in the back of a car with the engine running and aircon on while the mother did some shopping."
Irwin said she was stunned that the mother did not think she had done anything wrong when she returned to the vehicle.
"While the child was not distressed, it took some time for the mother to return to the car and police were called but she had left before officers arrived."
Irwin said these matters were treated "very seriously" and the mother's description and vehicle details were given to police.
Security guards at the centre regularly checked vehicles for any unattended children or animals, Irwin said.
"We take a zero-tolerance approach no matter what time of year it is," she said.
Papamoa Plaza manager David Hill said there had been the odd dog left inside a vehicle a few times a year but no incidents of unattended children during his long tenure.
"The practice of leaving any child alone is unacceptable. While we prefer to take an educative response in the first instance, we will call the police if the situation warrants it."
Bayfair Shopping Centre manager Steve Ellingford said there had been no recent reports of children being left in cars, however the centre also had a "zero-tolerance" policy.
"The child's safety is our first concern."
Ellingford said any parent returning to their vehicle was asked to stay until police arrived.
"If they refused to stay we will pass on the vehicle details to the police for them to follow up with the parents."