Mr Power was suspended from duty in November 2008
A public inquiry cannot be held into the suspension of Jersey's police chief while a British police investigation is under way, the chief minister has said.
Graham Power was suspended in 2008 amid allegations about his handling of the historic abuse enquiry.
Deputy Bob Hill wants to find out on what grounds Mr Power was suspended.
Chief Minister Terry Le Sueur said that would have to wait until after Wiltshire Police finished investigating how the abuse enquiry was handled.
In 2006, the island's police began investigating abuse claims at children's institutions and in private homes dating from the early 1960s to the 1980s.
Mr Power, who was the island's chief officer of police when the investigation was set up, was suspended from duty on full pay in November 2008.
Since then, no further disciplinary action has been taken and he denies any wrongdoing.
Deputy Hill wants the States to appoint a committee to fully investigate, in public, why and how Mr Power was suspended.
One of the things he wants to find out is on what grounds the then Home Affairs Minister Deputy Andrew Lewis made the decision to suspend Graham Power.
Chief Minister Le Sueur said that had to stay confidential until the Wiltshire Police investigation was completed.
Mr Le Sueur also wants to appoint just an individual commissioner to investigate the case.
Deputy Hill said he believed that a commissioner's review would be too secretive, which is why he wants a committee.