Investigators traced the call to Vancouver, Washington, but based on the timing of other sightings, they don't believe Dorner was in Vancouver at the time, the affidavit states.
Days later, early Thursday morning, Dorner allegedly opened fire on two LAPD police officers, wounding one, in the suburban city of Corona.
Roughly 20 minutes later, Dorner allegedly fired on two officers in the nearby city of Riverside, killing Crain and wounding another.
Since then, the LAPD has provided security and surveillance details for more than 50 police officers and their families -- many of whom were named in the manifesto.
Additionally, the LAPD is no longer releasing the police chief's schedule to the public or the media.
'Ghosts' of the LAPD's past
It was Dorner's allegations of racism at the LAPD that led Beck over the weekend to reopen the investigation into his claims.
Beck said he was not doing it to "appease a murderer" but out of concern that Dorner's allegations will resurrect a painful part of the department's history.
For years, the LAPD was dogged by complaints of racism and corruption. In 1965 and 1992, the city was rocked by racial riots that were sparked, in part, by claims of police racism and brutality.
"I hear the same things you hear: The ghosts of the past of the Los Angeles Police Department," Beck said Sunday. "I hear that people think maybe there is something to what he says, and I want to put that to rest."
Despite numerous reviews of Dorner's case, he said it has "never been reviewed by me."
"If there is anything new, we will deal with it, and we will deal with it in a public way," Beck said.