Reeva Steenkamp may have been beaten with a cricket bat by Oscar Pistorius before shooting her

South African police believe that Paralympic athlete Oscar Pistorius may have beaten his girlfriend Reeva Steenkamp with a cricket bat before shooting her.

Detectives are reported to have recovered a bloodied bat from Oscar Pistorius’ bedroom and to have established that model Reeva Steenkamp’s skull had been “crushed”.

This and other evidence – a smashed bathroom door, a 9 mm pistol, the peculiar pattern of wounds on the body and reports of a row earlier in the evening – is said to have led them to believe the murder case against the sprinter is “rock solid”.

Reeva Steenkamp, 29, was shot four times early on Thursday at Oscar Pistorius’ luxury mansion in a secure housing estate on the outskirts of Pretoria.

Police have rubbished speculation that Oscar Pistorius – who is known to have kept a pistol by his bed and a machine gun at his bedroom window – may have mistaken his girlfriend of three months for an intruder.

Prosecutors have formally charged Oscar Pistorius with premeditated murder but the Blade Runner’s family say he firmly denies such a charge.

Yesterday it emerged that he called his close friend Justin Divaris shortly after the killing – reportedly before the emergency services were alerted – and told him: “There has been a terrible accident, I shot Reeva.”

Justin Divaris rushed to the sportsman’s house, where he said Oscar Pistorius repeatedly told him: “My baba, I’ve killed my baba. God take me away.”

While no officials would comment publicly on the case, a disturbing – though disputed – picture of what may have happened in Oscar Pistorius’ home started to emerge.

Neighbors have said they heard shouting coming from the house at around 1.30 a.m. There were some suggestions, quickly denied, that the row may have been about Reeva Steenkamp’s friendship with a rugby player.

At around 3.20 a.m., four shots rang out – apparently not all at once. The first person Oscar Pistorius called was his father Henke, 59.

When Henke Pistorius arrived, he allegedly saw his son carrying his nightie-clad girlfriend down the stairs.

She had been shot in the head, hip, arm and hand. Pistorius – and later paramedics – struggled in vain to save Reeva Steenkamp’s life.

Police reportedly found the bloodied cricket bat in the bedroom. The en-suite bathroom door was riddled with holes, a pistol holster was found by oscar Pistorius’ bed and a gun cartridge was on the floor.

South Africa’s City Press quoted an unnamed police source as saying: “The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and locked herself in the toilet.

“She was doubled over because of the pain. He fired three more shots. She probably covered her head, which is why the bullet also went through her hand.”

The source said police are carrying out tests to establish whose blood is on the bat.

While one scenario is that Oscar Pistorius attacked Reeva Steenkamp with the wooden bat, it has also been claimed that the model may have used it to defend herself.

A third possibility is that Oscar Pistorius used it to break down the bathroom door. Those close to Oscar Pistorius have suggested that he may done so in a bid to “save” his dying girlfriend.

According to this theory, the athlete first shot Reeva Steenkamp by accident, whereupon she fled to the bathroom. He then shot at the door lock to try to get in, accidentally killing her.

Oscar Pistorius’ father appeared to suggest it is this version that he believes.

While he admitted that he had not talked to his son in detail about what happened, he said he had “zero doubt” that the sportsman thought Reeva Steenkamp was an intruder.

A more likely defence from Oscar Pistorius is to acknowledge that there was a row but that he did not intend to kill her.

Some in South Africa have speculated about the nature of Reeva Steenkamp’s friendship with Springbok rugby player Francois Hougaard, and whether this played a part in the tragedy.

Francois Hougaard, 24, was keen to distance himself from such reports at the weekend. His agent said: “This whole sad ordeal has got nothing to do with him.”

Last night Oscar Pistorius’ agent said he had withdrawn him from all planned races but insisted his sponsors were sticking by him.

The tragedy has also cast fresh light on Oscar Pistorius’ apparent attraction to danger and weaponry.

As well as owning a pistol and machine gun, at the time of Reeva Steenkamp’s death he reportedly had seven outstanding firearm licence applications.

One was for same type of assault rifle used in the recent Sandy Hook school massacre in the US.

Oscar Pistorius, who was charged with premeditated murder at a court appearance on Friday, spent the weekend in a police cell ahead of a second hearing planned for tomorrow at which his lawyers are expected to ask for bail.

Police say they will oppose the request.