Police Minister Anne Tolley had previously said Mr Bush's comment about Mr Hutton's integrity was quoted from his police record. Mr Mallard disputed this.
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.