The actor's ex-girlfriend alleged he punched her "more than once" back in January

The drama between Mel Gibson and ex-girlfriend Oksana Grigorieva has now caught the eye of the police.

“An investigation of domestic violence was launched by [Los Angeles Sheriff’s] Malibu/Lost Hills station detectives … involving actor Mel Gibson and his former girlfriend Oksana Grigorieva,” read a statement released Thursday. “The detective in charge of the investigation is currently gathering information regarding the allegations. Due to the investigation being preliminary in nature, no other information is available at this time.”

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The statement refers to an incident between the couple occurring on Jan. 6, 2010.

Attorneys on both sides weren’t immediately available for comment.

According to Los Angeles Sheriff’s Department spokesman Steve Whitmore, police began investigating after being contacted by Grigorieva. “The allegations were brought to our attention from the alleged victim,” he says. “We interviewed her on Monday. We were first contacted several days before that. When the investigation is completed, which could take up to a month, we will then turn the case over to the district attorney’s office for consideration, which is a routine procedure.”

Gibson, 54, and Grigorieva, 40, have been locked in a bitter custody dispute over their 8-month-old daughter, Lucia. The Russian singer alleged in a restraining order filed June 25 that the actor punched her in the face “more than once” on that date in January, causing a broken tooth, knocking out a veneer and causing a concussion.

Sources close to Gibson have denied the allegation, claiming he merely was trying to stop Grigorieva from shaking Lucia “like a ragdoll.”