Oscar Pistorius Murder Investigation -- Bloody Cricket Bat Found at Scene

A blood-spattered cricket bat is now the center of the investigation into the shooting death of Oscar Pistorius' model girlfriend ... this according to a newspaper in South Africa.

Cops are unsure if the bat was used by Reeva Steenkamp in self-defense or if Pistorius used it in his attack -- either directly hitting Steenkamp with it or in an effort to break down a door.

The City Press, a paper in South Africa, says that Steenkamp's skull was crushed in addition to the gunshot wounds. The City Press quotes a source as saying, "There was lots of blood on the bat. Forensic tests will show whose blood it was."

It was also reported Sunday that Pistorius' first call following the shooting was not to police, but rather his friend, Justin Divaris, who told The Mirror, "I said to him, ‘What are you talking about? I don’t understand you?’ He then repeated himself, ‘There has been a terrible accident, I shot Reeva.'"