Arms Act 1983, s 3(2)(ii)
Yes, they can and they do, in their vehicles.
New Zealand police officers are legally entitled to carry firearms, because the restrictions in the Arms Act that apply to the general public don’t apply to the police (in the same way that they don’t apply to the New Zealand military).
Despite the popular perception that New Zealand has an unarmed police force, police policy and practice is for all police vehicles to carry firearms in locked cabinets. So while New Zealand police officers don’t carry firearms on their hip, they do all have firearms readily available to them, that they can usually access within seconds.