In a sworn declaration dated June 23, 2010, Gibson, 54, recalls the altercation at one of his Malibu, Calif., homes in January that prompted police to launch a domestic violence investigation.
But the actor-director says Grigorieva grabbed Lucia, 1, out her of bassinet and eventually ran out into the backyard, according to TMZ.com, which obtained the court documents.
Gibson says Grigorieva, 40, ran for nearly 75 yards across bumpy, dimly lit ground with Lucia in her arms. When she came back into the house, Gibson claims Grigorieva was "hysterical" and her "rapid movements were causing Lucia's little body to be flung from one side to the other, her head shaking violently."
Fearing shaken baby syndrome as Grigorieva would not hand the baby over and was continuing her "rough and erratic movements," Gibson said he had to act.
"I slapped Oksana one time with an open hand in an attempt to bring her back to reality," Gibson said. "I did not slap her hard. I was just trying to shock her so that she would stop screaming, continuing shaking Lucia back and forth."
But Grigorieva has maintained she was punched in the face more than once, resulting in visible bruising. She later told PEOPLE of that night, "I thought he would kill me."
Gibson, however, refutes her version of events.
"I did not hit Oksana with a closed fist, as she alleges," he said. "I did not ever punch her in the face or in the temple or anywhere else, not then or at any other time."