Oksana Grigorieva told Sheriff's deputies Mel Gibson threatened her with a gun ... TMZ has learned.
TMZ broke the story ... the L.A. County Sheriff's Department is investigating Mel for alleged domestic battery, assault with a deadly weapon and child endangerment.
-- Domestic Violence: Oksana told Sheriff's deputies Mel punched her in the face twice, knocking out a tooth and chipping another one. Mel -- through his lawyers -- has denied it.
-- Assault with a Deadly Weapon: Sources tell TMZ Oksana told deputies Mel threatened her with a handgun at his Malibu estate. Sources say the allegation is solely based on Oksana's word.
-- Child Endangerment: We're told Oksana claims on January 6 of this year Mel allegedly punched her while she was holding their baby.
As TMZ first reported, Mel's lawyers will present evidence to Sheriff's deputies that Oksana made up some of the stories and tried to extort him by demanding cash in return for the secretly-recorded tapes.
We're told the Sheriff's Department will present the case to the L.A. County D.A.'s Office for felony review ... probably in 2 weeks.