The 29-year-old model was alive after she was shot and was carried downstairs by Pistorius, who was arrested and charged in her Valentine's Day death, the official said Monday, speaking anonymously because he was not authorized to release details to the media.
Pistorius, 26, a double-amputee national sports hero nicknamed "Blade Runner" because he runs on prosthetic legs, denies killing Steenkamp, a law school graduate, in his house in an upscale gated community on the outskirts of Pretoria, South Africa's administrative capital.
He is charged with murder.
Investigators said an iPad found at the house, along with phones belonging to Pistorius and Steenkamp, were being examined for clues, Britain's Daily Telegraph reported.
A bloody cricket bat is considered key evidence in the case, Johannesburg's City Press newspaper reported.
Detectives were trying to determine whether the bat was used to attack Steenkamp or if she used it in self-defense. Investigators were looking into the possibility that Pistorius used the bat to break down the bathroom door.
City Press said police ordered Pistorius' blood tested for drugs and anabolic steroids in case they need to see if any alleged aggressive behavior might be associated with having taken large steroid doses -- a condition sometimes called "'roid rage."
Pistorius was scheduled to appear in court Tuesday for a bail hearing, CNN reported. South African prosecutors have said they intend to upgrade the charge against him to premeditated murder.
Also Tuesday, Steenkamp is to be buried in a private service in Port Elizabeth, her hometown.
Pistorius said he canceled all of his race plans.
"I have decided that following these tragic events that we have no option but to cancel all future races that Oscar Pistorius had been contracted to compete in," he said in a statement read by his agent, Peet van Zyl, Sunday.
Pistorius has contracts to race in Australia, Brazil, Britain and the United States, van Zyl said.
The action will allow Pistorius to "concentrate on the upcoming legal proceedings," he said.
Sponsors and partners have agreed to maintain their contractual commitments as the legal process continues, he said.
The sprinter's father, Henke Pistorius, told Britain's Sunday Telegraph his son, a gun enthusiast, had accidentally shot Steenkamp, thinking she was an intruder.
"When you are a sportsman, you act even more on instinct. It's instinct -- things happen and that's what you do," the older Pistorius said.
The shooting sent shockwaves through South Africa, where Pistorius had hero status because he was the first disabled athlete to compete in the able-bodied Olympic Games. He competed in the London Games as well as winning two gold medals in the Paralympic Games.
Francois Hougaard, a South African national team rugby player, has denied published reports that his "close relationship" with Steenkamp may have caused trouble between the model and Pistorius, the Telegraph said. He said the three were friends.