The man known as Case M, whose alleged breaches of Covid-19 directions contributed to the Government's latest lockdown decision, has not been referred for prosecution.
A police spokeswoman said people could be investigated if they fail to follow specific orders from health officials to self-isolate.
She said police could get involved if the Ministry of Health supplied officers with relevant information.
"At this stage, we have not received referrals and we continue to focus on working with individuals, whānau and communities to support them to isolate and be tested.
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"Police will continue to work with Public Health as we have to date, including to assist finding people who should be isolating and who prove difficult to find."
Asked about consequences for people who breached self-isolation advice, Prime Minister Jacinda Ardern today said the man already faced the entire country's judgment.
She said politicians should not interfere in New Zealand's independent law enforcement, and any decision about prosecution was for police.
Ardern rejected claims Case M and his family were not kept in the loop about obligations to self-isolate or otherwise follow health advice.
"This case has demonstrated what the ramifications can be," she told a Monday afternoon press conference.