Police are urging people to be cautious if they receive an email claiming to be from the organisation.
Police said they had received several reports of scam emails claiming to be them or other justice sector partners and inquires were underway.
The emails claimed to have located explicit illegal material on the recipient's computer and said an arrest warrant would be issued if the person does not reply.
Police said the emails were a scam and anyone who received one should not reply under any circumstances.
"Although some versions of the email do not specifically reference money, other similar scams involve the recipient being issued a 'fine' when they respond," police said.
"Police recommend taking a cautious approach to unsolicited emails. Trust your gut instinct - if it doesn't feel right, it probably isn't."
They said police and other government agencies would never contact people out of the blue and ask for passwords, credit card or bank details.
Anyone who received such an email was asked to forward it to the police cyber crime team by emailing cybercrime@police.govt.nz.