National wants the head of an inquiry into Wally Haumaha's appointment as deputy police commissioner to step down or be sacked.
Pauline Kingi is leading an investigation into the process that led to Mr Haumaha being made deputy police commisssioner - despite comments he made defending police officers accused of rape in 2004.
Dr Kingi has endorsed 23 of Mr Haumaha's skills on the professional networking platform LinkedIn, including law enforcement, crime prevention and leadership development.
National's police spokesperson Chris Bishop said that constituted a conflict of interest and she must go.
"She simply has no credibility to chair the inquiry. It's a blatant conflict of interest, she must stand down or Tracey Martin must sack her," he said.
Ms Martin is the minister overseeing the inquiry, and said Dr Kingi signed a form declaring there was no conflict of interest.
She said she had also made known the two occasions where she met or was in the same vicinity as Mr Haumaha.
"Dr Kingi has declared that she knew Mr Haumaha in a professional capacity when she was a highly respected public servant. She has also declared that she attended a tangi either in 2015 or 2016," Ms Martin told Parliament.
She said Dr Kingi was doing work with Māori and the police, which Mr Haumaha was also involved with, and they both attended that same tangi.
Ms Martin said she was frustrated that National had sunk to this level.
"A LinkedIn profile, a networking digital platform, that somehow is supposed to be the judge of a person's character? Have you seen this lady's CV?" she asked.
Ms Martin said the suggestion that liking somebody on Facebook or endorsing them on LinkedIn made somebody unqualified was frustrating.
Acting Prime Minister Winston Peters described LinkedIn as a career enhancing utility. He said everyone endorsed everyone else, and the only person that had not been endorsed happened to be himself - because he did not have a profile.
Mr Peters said he had complete confidence in Dr Kingi and the process.
"It's not like writing a fully-fledged reference, and sending it off with a signature on it. It's social media after all and you know how skitterish that can be."
Ms Martin and Mr Peters both made the point that the inquiry is into the process of the appointment, not the person.
The inquiry has been established to find out why Mr Haumaha's past comments regarding a sexual assault case either weren't discovered or weren't disclosed to the minister by the State Services Commission, during his appointment process.
But Mr Bishop did not believe there was a differentiation to be made.
"He is at the centrepiece of that inquiry. She has a relationship with the centrepiece of the inquiry. I just don't think it's credible that she stays on in the role," he said.