Kate Major told police Michael Lohan threatened to kill her, called her a "c**t" and kicked her in the face ... this according to a police report and formal complaint obtained by TMZ.
According to Kate's complaint she says, "My fiance Michael Lohan came home while I was sleeping in a sofa chair. He woke me up, yelling, 'Why didn't you pick up your cell phone, you stupid c**t.'"
Kate continues, "He then turned over the chair while I was still in it, tossing me to the floor. I crawled to the other side of the room to get away from him. He walked over to me, took his shoe off and kicked me in my face while I was still on the ground. He stood over me and said, 'I'm going to go back to jail cause of you, cause I will kill you.'"
Kate says, "He said all of this to me cause he is afraid I'm going to leave him. I am very afraid of him."
According to the police report, which parrots Kate's handwritten complaint, cops say, "Minor swelling observed on [her] lip."
Major said when she fell out of the chair she bumped her head into the wall and body on the floor and complained of a cut lip, a sore left collarbone and a scraped right knee.
Michael says there was an argument but denied touching Kate.
UPDATE: Lohan is scheduled to appear in court on August 18 to be arraigned on harassment charges.