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.