The police investigation is of the three months from April to June 2014, a year in which Waitemata police issued more than 194,000 speed tickets, the most in the country at more than 16,000 a month.
Last year, about $71 million was paid in fines, mostly for speeding.
The Herald on Sunday understands some officers involved have sought legal advice as police consider criminal investigations.
Police refused to answer whether any other officers have been disciplined in the past week.
A spokesperson for the New Zealand Police Association would not comment on whether it was supporting any of the officers.
The Independent Police Conduct Authority did not respond to queries about whether it had requested information from police.
The overall investigation centres on allegations officers failed to record how and when the devices were calibrated. Hand-held speed cameras need to be calibrated and tested before use to ensure they record accurately.
Superintendent Bill Searle, of the Waitemata District, last week said it was a "procedural failure" by a small number of staff and there was no evidence to suggest the cameras were inaccurate.
Road-policing staff nationwide had been reminded of their obligations regarding correct reporting and regular audits were being carried out, he said.
Of the three officers who have been disciplined, one is the subject of an ongoing employment matter, said Searle.
