A new taskforce has been set up to investigate the false information that was provided to contact tracers.
Police Commissioner Grant Stevens said the taskforce was made up of 20 detectives and analysts.
It will report twice daily to taskforce leader Peter Harvey.
Assistant Commissioner Harvey said at least one person had not told the truth and it would look at what, if any, legislation had been breached.
"I'm approaching this whole thing with an open mind," he said.
Assistant Commissioner Harvey said no stone would be left unturned and they would focus on any potential criminal activity.
"My obligation is totally different to being caught up in the emotion," he said.
"The importance of this is not lost on SA Police. If, in the end, there are (any charges possible) there will be and if there aren't there won't be.
"It may well be that there isn't any criminal offence.
Commissioner Stevens said he was satisfied the contact tracing team was not told the truth in the first instance.
"I'm sure the individual is reflecting on the statements they made," Mr Stevens said.
He said his initial legal advice was that, while people were obligated to provide information at a contact tracer’s request, there was no penalty for a lie.
"My understanding is they can’t be arrested or charged, but my team will look at any mechanism whatsoever," he said.