Essex chief constable Jim Barker-McCardle said it was vital investigations continued to establish what led to the double shootings which left Pc Ian Dibell dead and another man injured.
He was speaking after Peter Reeve, 64, was found dead in a churchyard in the village of Writtle near Chelmsford. Reeve is believed to have shot himself.
The force had launched a major manhunt and warned residents to stay indoors after Reeve ran amok in a residential street in the seaside town of Clacton, Essex, on Monday afternoon.
Dibell was killed as he tried to intervene. He has been described as a hero by colleagues.
Another man, named locally as Trevor Marshall, is in hospital with leg injuries.
The police chief said officers were following a number of lines of inquiry as to the motive for the attack.
Neighbours suggested there may have been a dispute over car-parking which spiralled out of control.
Barker-McCardle said Dibell, who lived near the crime scene in Redbridge Road, had “paid the ultimate price” after stepping in to protect a member of the public while off duty.