South African police found a bloodied cricket bat at the home of Oscar Pistorius following the Valentine's Day killing of his model girlfriend, a newspaper reported yesterday. The star Olympian and Paralympian athlete was charged on Friday with the murder of 29-year-old Reeva Steenkamp, who was shot dead at his luxury Pretoria home in a case that has gripped the world. His father said in a newspaper interview published yesterday that there was "zero doubt" his son had mistaken the blonde cover girl for an intruder, a suggestion that police have dismissed. Police sources close to the investigation told South Africa's City Press newspaper that Steenkamp's skull had been "crushed". One source said: "There was lots of blood on the bat." Police are investigating whether the bat was used to assault Steenkamp, who was shot four times in the early hours of Thursday, or if she used it to defend herself. "The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and hid herself in the toilet … He fired three more shots," a police source told the City Press . The paper said Pistorius could have experienced aggressive behaviour linked to taking large doses of steroids, describing the case against him as "rock solid". Other reports suggested there had been a fight between the two lovers that had spilled over from Wednesday night, when neighbours called security guards complaining about a "commotion" inside Pistorius' house. Police refused to officially comment on the case. Pistorius - a national icon who inspired people around the world when he became the first double amputee to compete against able-bodied athletes in the Olympic Games last year - is spending the weekend in a police cell. He is due to apply for bail at a new court hearing tomorrow, the same day a memorial service will be held for Steenkamp in Port Elizabeth, her hometown on South Africa's southern coast. Henke Pistorius, 59, told British newspaper The Sunday Telegraph that the family had "zero doubt" his son had shot Steenkamp on instinct after mistaking her for an intruder. "When you are a sportsman, you act even more on instinct," he said. "It's instinct - things happen and that's what you do." Police have said there had been several previous domestic incidents at Pretorius' home. The City Press report said Steenkamp was wearing a nightdress at the time of the killing and that the bed was rumpled.