The chief constable of West Yorkshire police should be suspended pending investigation of his conduct during the 1989 Hillsborough disaster, a Merseyside MP has said.

Maria Eagle, the Labour MP for Garston and Halewood, said she was surprised that Sir Norman Bettison, an inspector in South Yorkshire at the time, had not suspended already.

Bettison, who has said he has nothing to hide, has been referred to the Independent Police Complaints Commission (IPCC) over allegations that he gave misleading information following the disaster in which 96 Liverpool football fans died.

Last month's report from the Hillsborough independent panel uncovered a police cover-up that appeared to shift blame for the tragedy on to the victims. It revealed that 164 police statements were altered, 116 of them to remove or change negative comments about the policing of the FA Cup semi-final between Liverpool and Nottingham Forest.

Eagle has long campaigned on the Hillsborough issue, and in parliament in 1998 she accused Bettison of being part of a "black propaganda unit" that smeared fans – a claim that he has always denied.

Eagle told BBC News she was concerned that "when he retires – because he was chief constable of Merseyside at one point – people of Merseyside, including the bereaved families and those who've been traumatised on the day, will be paying his pension through our council tax. Now that's not something that I think is right."

Bettison, 56, has said he plans to retire in March. Last month Eagle accused Bettison of inconsistencies in his version of events.

The IPCC investigation into allegations of misconduct by South Yorkshire police, West Midlands police and others will be the biggest ever inquiry into the police in the UK. Both serving and former police officers – as many as 200 – will be investigated, the IPCC said. The Crown Prosecution Service has said it will also consider bringing criminal charges.

The IPCC said the allegations against Bettison would be investigated. "This is a serious allegation. We will independently investigate it," it said.

In a statement last month, Bettison said his role was never to "besmirch" fans, and said he was "deeply sorry that impression and slight has lingered for 23 years". But he added: "There is nothing that I am ashamed of."