Police Minister Anne Tolley says it would not have made any difference if she had been told about problems with police statistics by her colleague Judith Collins two months before the police investigation, and three months before police told Mrs Tolley.
But Labour says this shows that neither minister was prepared to do her job.
The exchange follows revelations that five officers in southern Counties-Manukau wrongly re-coded about 500 burglaries between 2009 and 2012.
Labour used Question Time yesterday to ask whether Ms Collins had acted appropriately.
She heard rumours about issues with statistics and one of the officers involved in February 2012, but did not tell police or Mrs Tolley, who had just become Police Minister.
Police started investigating two months later, and the Deputy Commissioner and now Police Commissioner Mike Bush briefed Mrs Tolley on May 21, 2012.
Mrs Tolley said if Ms Collins had told her - three months before her first briefing with police on the matter - it would not have made any difference.
Labour's police spokeswoman, Jacinda Ardern, said it was remiss of Ms Collins not to pass on information, especially as she was a former Police Minister and the local MP where the statistics were manipulated.
"So [Mrs Tolley] is saying it wouldn't have made any difference, because neither of them would have done their job, anyway."