Committee chairwoman Jacqui Dean is unhappy with the way Trevor Mallard and Phil Goff behaved during the appearance of Police Commissioner Peter Marshall and Deputy Commissioner Mike Bush.
Labour MP Trevor Mallard stormed out of the committee during a fiery exchange about the eulogy given by Mr Bush at the funeral of former detective inspector Bruce Hutton in April.
Mr Bush told mourners that Mr Hutton, who was found to have planted evidence in a murder inquiry, had "integrity beyond reproach".
At the committee Mr Marshall said he "absolutely" supported Mr Bush's attendance at the funeral and his eulogy, saying
"You have to remember this was a funeral service attended by grieving family, by grieving friends and associates of the deceased and he made those comments in the context of that particular set of circumstances".
Ms Tolley tried to have Mr Mallard's questions on the subject ruled out of order, because the Labour MP appeared to say Mr Bush should be sacked.
"We are deciding whether or not continue [Mr Bush's] salary. That's what we're deciding now," Mr Mallard said, before storming out of the hearing.
Mr Goff argued with Ms Dean and swore after his questions about police redundancies and station closures were stifled.
Mrs Dean said both outbursts were unacceptable.
Speaker David Carter will determine if there's a case to answer before the matter goes any further.
Mr Mallard said: "The only comment I will make is the fact that Jacqui Dean has been public [about the complaint] is an indication that she's not taking it seriously.
"You either let the Speaker decide if you've got a case or you make a fuss about it publicly, you don't do both," he said.
