"We have received a credible piece of information that the gun could have been disposed of in this area," he said. "The offender could have run or driven here and discarded the gun."
He said police were using metal detectors to search the stream and surrounding area for the gun which was believed to be a .22 calibre, sawn-off rifle.
Mr Anderson said the area had been re-searched and despite the fact the gun would have been disposed off 36 years ago, police believed it could still be in the area as the stream hadn't changed much over the years.
He said it would also still be possible to get forensic evidence from the gun.
The stream which is being searched is about 1km long.
"It is dirty work and the divers are sifting through mud and silt. The dive team are clearing the stream bed and there are volunteers who are searching the surrounding area," he said.
"It is possible that someone has seen this or someone has even taken it home and we want to hear from them."
Mr Anderson said police had received numerous calls on the hotline which had been set up to help the investigation.
"People from around the country have come forward with information," he said.
"Some of those are people we haven't heard from before and other were part of the initial investigation."
Mr Anderson said he was positive police were making progress on the case and he was confident they would find the person responsible.
Mr Percy's death is thought to be one of the country's oldest unsolved cases and police this week announced it had been re-opened because they had received new leads.
The ANZ bank where Mr Percy worked was first targeted by a robber on July 16, 1976. The offender then tied up two tellers and Mr Percy before taking about $13,000.
Four months later, on November 5, the bank was subjected to a second robbery.
Mr Percy was again on duty and tackled the offender. He was shot twice and died on the way to hospital.
Anyone with information about the case should call police on 0800 4 PERCY or email operation.percy@police.govt.nz.