Detectives are working to establish what prompted a man to shoot dead an off-duty police officer before going on the run and apparently turning the gun on himself.
Essex Police said a "live murder inquiry" is continuing into the murder of Pc Ian Dibell and reiterated calls for witnesses to come forward.
The plea came after prime suspect Peter Reeve, 64, was found dead in a village graveyard 17 hours after the killing. His body was discovered alongside a weapon close to a rural church in Chelmsford and investigators believe he took his own life.
Police launched a major manhunt and warned residents to stay indoors after Reeve armed himself with a gun and ran amok in a residential street in the seaside town of Clacton, Essex, on Monday afternoon.
Pc Dibell is believed to have challenged the gunman before being shot dead, while another man, named locally as Trevor Marshall, 48, was taken to hospital after suffering leg injuries.
Teams of armed officers were drafted in to join the manhunt and a picture of Reeve was circulated by police after he dumped his car near the crime scene and fled.
The search was finally called off after his body was found by a member of the public at All Saints Church in Writtle, near Chelmsford, at around 8.30am on Tuesday. The spot is around 40 miles away from the murder scene and detectives are working to establish how Reeve travelled there.
The suspected killer, reported to be a retired bus mechanic who was largely unknown to the police and did not have a firearms licence, is understood to have had several family members living near the church and may have had a relative buried there. Police said they were in contact with his family.
Essex Chief Constable Jim Barker-McCardle said officers were following a number of lines of inquiry as to the motive for the shootings and that all possibilities would be examined. He added that there was no reason to suspect anybody else was involved in the killing.
Neighbours suggested the shootings may have been triggered by a local dispute over car parking which spiralled out of control. Other reports suggested that Reeve has become "paranoid" about a couple who were living in a flat below him, close to where the shootings took place in in Redbridge Road.