Capt. John McMahon told the paper that Shaw declined to be interviewed, and that, "In light of that, our investigation into a possible domestic dispute will continue."
He added that Shaw's girlfriend "did not indicate she was a victim" of domestic violence when she talked with police.
On Wednesday, Shaw admitted that the story of how he injured his ankles was a lie, USC annouced in a statement. The fifth-year senior initially told USC that he had jumped from a second-story balcony to save his nephew, who was drowning in a pool in Palmdale. The school published his heroic account on its website. but after Shaw told them that the story was not true, the university apologized, calling the initial account a "complete fabrication." Shaw was suspended indefinitely from all team activities but Trojans head coach Steve Sarkisian has not ruled out the player's return.
Shaw hired attorney Donald Etra on Wednesday. Etra told the Los Angeles Times that Shaw "has already spoken to the LAPD twice. We believe that is enough. The matter is over and there is no need to talk to them further. ... Enough is enough."
On Thursday, Etra said no criminal activity was involved in Shaw's injuries.
"The injury was caused by a fall from his balcony at his apartment," Etra told The Associated Press. "He is very remorseful. He accepted responsibility for telling the untruth. He has apologized to USC, and he's looking forward to putting this behind him."
The Los Angeles Police Department had confirmed that a man named Joshua Shaw was mentioned -- but not as a suspect -- in a report involving a break-in at a downtown apartment building Saturday night.
According to the LAT's report, this is how police say the incident over the weekend played out:
Police went to a third-floor apartment in the Orsini building in downtown Los Angeles about 10:40 p.m. Saturday night after receiving a report of a woman screaming, Officer Sara Faden said.
Officers knocked on the apartment door but there was no answer, Faden said. The officers then broke open the door and conducted a brief search, but found no one inside. Officers noticed that "the window had been pried open," she said.
Faden said witnesses told police they had seen a man with dreadlocks climbing from the third-floor balcony of the apartment. The woman who resides in the unit then arrived on the scene.
Given the description of the man provided by witnesses, she said it fit that of her boyfriend, Shaw, who has another apartment in the building.
The woman, whom police have not identified, reported nothing stolen from the apartment.
Shaw had four interceptions while starting 14 games last season, his second with the Trojans. He has played both safety and cornerback, moving around a defense with little depth due to NCAA sanctions.