They submitted evidence to the prosecuting authorities linking the killing of Barry Wallace, 18, of Kilmarnock, Ayrshire, to William Beggs, jailed for six years in 1991 for a knife attack on Brian Quinlan, whom he met at a gay nightclub in Glasgow.
Police patrols in Kilmarnock have been stepped up and local people have been advised not to go out alone after dark and to avoid contact with strangers. Last Wednesday, Mr Wallace's head was discovered on an Ayrshire beach, 10 days after one of his limbs was found in Loch Lomond, 80 miles away.
Mr Wallace's torso has not yet been found and it is not known at what point he died after going missing.
In 1987, Beggs, who lives in Kilmarnock, was sentenced to life imprisonment for murdering Barry Oldham, 28, whose body was found on the North Yorkshire moors. At his trial, Beggs had pleaded self-defence, claiming Mr Oldham had made homosexual advances during a camping trip.
During his 1987 trial at Teesside Crown Court, Beggs additionally faced a number of charges of unlawful woundings relating to students and a retired head teacher. He was convicted on two of these counts. However, the murder conviction was quashed in 1989 because the appeal court decided that Beggs' trial had been seriously prejudiced by the trial judge's decision to allow the jury to hear details of the other wounding charges.
Beggs, 36, was last seen near his home two days before it was raided with battering rams by police on Friday. Since then the former council house has been sealed off by police. Beggs, originally of Co Down in Northern Ireland, moved to Kilmarnock in 1990.
There he became a housing officer with Kilmarnock District Council and was living in his present home when Mr Quinlan escaped naked from his first-floor window covered in blood after being attacked.
Beggs' whereabouts are unknown and last night Strathclyde Police would neither confirm nor deny that he was their prime suspect.
In a three-line statement a spokesman noted merely that a report had been submitted to the Procurator Fiscal "in respect of a named individual". Under Scottish law, the police are required to keep the Procurator Fiscal notified of developments in a criminal investigation.
A spokesman for the Crown Office in Scotland declined to explain why the police had yet to circulate a photograph of Beggs or a description of him even though, it is understood, other police forces are seeking the suspect.
It is also not known why Beggs did not become the focus of police attention until Friday, nearly a fortnight after the first body parts were discovered in Loch Lomond. Mr Wallace was reported missing on 6 December after he failed to return home from a night out.