Police are said to be investigating several situations by which the bat may have been used in the incident, South Africa's City Press reports.
"There was lots of blood on the bat. Forensic tests will show whose blood it was," a source claimed.
Steenkamp's skull was reportedly crushed in the incident, and tests are being undertaken to ascertain how she sustained the injury.
Additionally it is claimed that Steenkamp was wearing a nightie at the time of the shooting, that her iPad and overnight bag were on the bedroom floor and that both she and Pistorius had slept in the bed that night.
A gun cartridge was reportedly found in the bedroom and 9mm holster on Pistorius's side of the bed.
"The suspicion is that the first shot, in the bedroom, hit her in the hip. She then ran and locked herself in the toilet," the source continued.
"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."
Police have also taken blood from Pistorius to be tested for the presence of drugs.
Pistorius is alleged to have told his sister Aimee that he had mistaken Steenkamp for a burglar.
The Paralympian has denied murder "in the strongest terms" and remains in police custody until his postponed bail application is heard tomorrow (Tuesday, February 19).
He is said to be on suicide watch as he awaits the hearing.