Oksana Grigorieva and Mel Gibson
FayesVision/WENN
The Oscar winner, 54, and the Russian musician-singer, 40, had been together about a year by the time they broke up in April 2010.
While at the time of the split a friend of the couple told PEOPLE, "They're still friends and they'll both raise Lucia together," since then their relationship has become less amicable.
Though the legal documents, which were filed Thursday in Los Angeles Superior Court, are sealed, RadarOnline, which first broke the story, reports that the main issue involves Gibson's access to the child.
Gibson, who just completed filming How I Spent My Summer Vacation, resides in Malibu. Grigorieva, meanwhile, is still living in a Sherman Oaks, Calif., home owned by Gibson – and has been doing so since their split.
She was reportedly served the legal papers there.
Gibson's rep has no comment.
In April 2009, Robyn Moore, the actor-filmmaker's wife of 30 years, filed for divorce from Gibson, citing irreconcilable differences. Later that same month, he and Grigorieva made their first public appearance together as a couple.
In addition to Lucia, Gibson is the father of seven children – six sons and one daughter – while Grigorieva has a son, Alexander, with her former boyfriend, British actor (and short-term James Bond star) Timothy Dalton.
• With reporting by ELIZABETH LEONARD
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