The officers under investigation are stationed at Auckland's Harbour Bridge motorway traffic unit under the Waitemata police district.
The investigation concerns three months from April to June 2014 - a year in which Waitemata police issued more than 194,000 speed tickets, the highest number in the country at more than 16,000 a month.
Last year, almost 82,000 speeding tickets were issued nationally each month by hand-held and fixed cameras. About $71 million was paid in fines, mostly for speeding.
Police refused to say exactly how many officers are involved or how many tickets they issued during the three-month period in question.
The Herald on Sunday can reveal the investigation centres on allegations the 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 accurately record speed and distance.
Police confirmed they were alerted to "reporting irregularities of three staff" in August 2014.
Superintendent Bill Searle, of the Waitemata District, said that it was a "procedural failure" by a small number of staff and there was no evidence to suggest the cameras were inaccurate.
"This has been confirmed by further testing carried out by the national police calibrations laboratory in Wellington," he said.
Traffic law expert Steve Cullen, of Albion Chambers, said the fact police had sent the devices to Wellington to get certification suggested there was cause for doubt.
As long as a certificate of accuracy was within 12 months of the date of offence, police could rely on it in court, he said. "It's a concern because each device is supposed to be certified as properly calibrated and operable. The only inference is they didn't have valid certification.
"It would only be if they failed to produce that certificate. Then the accuracy of their log books would clearly come into play because there would be a gap in the evidence."
Kelvin Davis, Labour spokesperson for police, said the incidents were "pretty sloppy".
"Why did it take so long to find out that police weren't following due process?
"They've left themselves wide open for challenge, which could well cost the taxpayer a lot of money," he said.
"What faith can the public have that police aren't taking shortcuts in other areas?"
Hand-held speed cameras have long been slammed as revenue gathering tools, though police say they are foremost a deterrent.
Searle said the procedural failings were not a wider training issue but specific to individual officers.
"We can't go into specifics regarding staff. While these inquiries are still ongoing but are satisfied at this stage that it is a small number and not indicative of a wider issue."
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.
If you know about this, contact amy.maas@hos.co.nz.