Gibson's publicist, Alan Nierob, would not elaborate beyond an apology Gibson issued Saturday in which the star admitted he uttered "despicable" things to deputies.
"I acted like a person completely out of control when I was arrested," the actor said in that statement. "I disgraced myself and my family with my behavior and for that I am truly sorry."
A leaked arrest report quoted Gibson as saying "The Jews are responsible for all the wars in the world," and asking an arresting officer, James Mee, "Are you a Jew?"
It's not the first time some have alleged Gibson is anti-Semitic. Some critics thought his movie, "The Passion of the Christ," blamed the Jews for the death of Jesus.
"I think that now, though, even people who gave him the benefit of the doubt at that time are thinking, 'Wow, maybe he really does believe this,'" People magazine Editor-at-large Jess Cagle told CBS News' The Early Show. "It's a real dichotomy between the way he behaved on Friday morning and what people see when they deal with him."
The entertainment Web site TMZ posted the document, which it said was four pages from the original arrest report. Harvey Levin, the reporter who first obtained the notes, told CBS News correspondent Vince Gonzales that the notes said Gibson was belligerent and attempted to flee. After being handcuffed, he allegedly also told the deputy he owned Malibu, before beginning a barrage of anti-Semitic remarks.
Sheriff's officials have declined to comment on Gibson's alleged remarks, but as Gonzales reports, the sheriff's department initially said Gibson was arrested without incident or special treatment.
"The sheriffs lied. They just flat out lied," Levin told CBS News.
The Office of Independent Review, a department watchdog panel, has opened an investigation into whether authorities tried to cover up Gibson's alleged inflammatory comments, said its chief attorney, Mike Gennaco. Sheriff's deputies have many of Gibson's statements and actions on tape, Gonzales reports.
"Assuming that the report was excised, then the question is was it done for a good reason within regulations," he said.
Gibson, a Roman Catholic, has filmed public service announcements for Los Angeles County Sheriff Lee Baca's relief committee dressed in a sheriff's uniform. Levin told CBS News he believes the department changed reports and covered up for Gibson because of his support for Baca.
"There is no cover-up," Baca told the Los Angeles Times. "Trying someone on rumor and innuendo is no way to run an investigation, at least one with integrity."
Gibson was arrested after deputies stopped his 2006 Lexus LS 430 for speeding at 2:36 a.m. Friday. Sheriff's spokesman Steve Whitmore said deputies clocked him doing 87 mph in a 45 mph zone.
A breath test indicated Gibson's blood-alcohol level was 0.12 percent, Whitmore said. The legal limit in California is 0.08 percent.