Police Minister Stuart Nash said he was not aware of the bullying allegations against Deputy Police Commissioner Mr Haumaha when he recommended him as a potential candidate for the role.
"My understanding is no formal complaint has been made at this stage, so let's wait and see what happens now," Mr Nash said on Thursday.
Three women involved in a joint justice project reportdely left Police National Headquarters (PNHQ) as a result of alleged bullying behaviour from Mr Haumaha.
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The policy analysts were based at PNHQ from October 2015 but all three left in June 2016, according to NZME, because they were feeling "devalued and disillusioned".
They told their managers about the behaviour and did not return to PNHQ, instead opting to work on the project from the Ministry of Justice offices, NZME reported.
The allegations come as a Government inquiry is underway into the appointment of Mr Haumaha as Deputy Police Commissioner.
His appointment was questioned after it emerged he called the alleged police rape of Louise Nicholas "nonsense" during an investigation in 2004.
During the police investigation in 2004 Mr Haumaha described Ms Nicholas' allegation of gang rape as "nonsense" and said "nothing really happened and we have to stick together".
Asked whether the inquiry should be widened because of the latest allegations, Mr Nash said that would be a decision for Cabinet to make.
"This is not an inquiry into any individual person. This in an inquiry into the process that led to the appointment of someone, and the sort of information that should be given when this sort of process is undertaken," Mr Nash said.
"The review is around the process of the appointment of a senior public official. It's not about the character of any individual," he said.
"I do expect all agencies to take allegations of formal complaints around bullying very seriously."
National Party police spokesperson Chris Bishop said the latest allegations are "deeply troubling and concerning".
"It comes on the back of further concerning revelations just a month ago about Mr Haumaha's conduct both in the past but also in recent years as well," Mr Bishop said.
"There are serious questions for Police Commissioner Mike Bush now, and also Police Minister Stuart Nash, about Mr Haumaha's appointment."
Mr Bishop said the Minister needs to say whether Mr Haumaha still has his confidence.
He said there are also wider questions for the departments of Justice, Corrections and Police about how the bullying allegations from the three women were dealt with.
"The question for Mike Bush is did he know about the allegations and did he know about the 2004 comments made by Mr Haumaha?"
In a previous statement Mr Haumaha apologised and expressed regret about the comments he made about Ms Nicholas.
"It is important to say outright that I take responsibility for those comments, I deeply regret them, and I unreservedly apologise for the hurt and concern they have caused," he said.
"In the 14 years since those comments, and particularly through the changes following the 2007 Commission of Inquiry, I have reflected deeply and often on what it means to live the values that New Zealanders rightly expect from their police."
Police have been contacted for comment about the bullying allegations and this story will be updated with any response.