Police Commissioner Mike Bush says his staff have encountered people who say "they are not even aware" of New Zealand's lockdown status.
He assured Newstalk ZB's Mike Hosking this morning they had made the comments with a straight face.
But he was sure most New Zealanders would obey the rules.
When asked how police would enforce the rules and make sure those out and about were out for a good reason, he said police officers may follow you.
"If they've got a good reason - if they're an essential worker or if they're going to the supermarket or if they're going to get food or health supplies - that's fine.
"If not, stay at home. That's how you're going to save lives."
'WE MAY HAVE A DRIVE...TO SEE WHERE YOU'RE GOING'
He said officers would have a fair idea of whether or not someone was going to the supermarket.
"We may even have a little drive with you to see where you're going."
Bush said their own workforce were being very strict about keeping up with hygiene practices.
Asked whether retired police officers may be recruited during this time, he said: "We're planning not to get to that stage, but we do have a few plans in stage."
Bush had a low key warning for people who if they did not stick to the rules: There would be consequences.
"We'll be the friendly face of police...until it needs to be something else, of course, if people don't comply."
He had earlier told Newstalk ZB's Chris Lynch that people shouldn't drive to the beach or a park for some fresh air once the lockdown starts.
He said people should only go out in their cars to get essential supplies.