A Killer Most Bizarre

The nearest police car arrived at White House Farm at about 3:45am on 7 August 1985 with the call sign, Charlie Alpha 7. On the way, they had overtaken a Citroen saloon driving at 25 mph. When the officers arrived, there was no one waiting for them despite their expectations. Three or four minutes later, the Citroen pulled up and out of it came Jeremy Bamber.
Earlier that evening, Bamber has called the police explaining that his father had called him saying that "his sister has gone mental. She has a got a gun." He reported that he heard a gun-shot and the line went dead. After ringing the line a few times, it came back dead. Bamber then called the police.
But did he commit the crime?