Fifty-nine-year-old Don Dunphy of Mitchells Brook was killed Easter Sunday by a member of the Royal Newfoundland Constabulary who has not been named.
The officer was investigating perceived threats on Dunphy's Twitter feed involving Premier Paul Davis and a cabinet minister.
The RCMP is investigating the death and has said the officer reported he shot Dunphy after the man aimed a rifle at him.
The Mounties say a loaded .22-calibre rifle was on the floor near Dunphy's body and was sent for testing at a forensics lab.
McCurdy says an independent inquiry would help restore public confidence in the police and could examine what led up to the shooting.