The alleged incident occurred Jan. 6 at an undisclosed location in Malibu, according to the sheriff's department, which lists the alleged victim as 40-year-old /*Oksana Grigorieva*/, Gibson's former girlfriend and the mother of his 8-month-old daughter.
"What we're trying to do is investigate, investigate, investigate, investigate, so when it's solid and stable and done we will then give that to the district attorney and they will do what they think is appropriate with our investigation," said Steve Whitmore, a spokesperson for the L.A. County Sheriff's Department.
Whitmore said detectives interviewed Grigorieva on Monday. She has been the only person interviewed so far.
Whitmore declined to disclose further details of the investigation or any potential evidence. The sheriff's department expects that its criminal investigation will take a month.
The couple, who split in April, has been involved in a nasty custody dispute over their infant daughter - the subject of a confidential court case.
Earlier this month, two entertainment websites reported the 54-year-old Hollywood filmmaker was caught on audio tape during a series of explosive arguments with Grigorieva. They say Grigorieva secretly recorded Gibson at the height of their breakup and custody fight.
Gibson reportedly went off on a tirade aimed at Grigorieva -- calling her an embarrassment, using the n-word, and making misogynist remarks. Another rant allegedly includes threats that Gibson would burn the house down.
The sheriff's department does not confirm anything contained in the web reports.
The custody matter is being heard by a judge in family court. All details, including the tape, are under seal.
The investigation is being conducted by the same sheriff's substation that arrested Gibson in 2006 on suspicion of drunken driving.
Gibson eventually apologized for making a series of anti-Semitic and sexist remarks during his arrest. He also said he had battled alcoholism for all of his adult life.
Gibson is no longer on probation for the drunken driving case and his conviction has been expunged.
The Associated Press contributed to this report.
