The woman, who police have not named, was subdued by a police officer who had joined the force two weeks earlier.
A passenger on Southwest Airlines Flight 4519 told KHOU-TV that the woman was behaving erratically throughout Sunday’s morning flight.
“She wrote ‘Help me’ and her name” on napkins, the traveller said.
“I knew something wasn’t right,” the passenger said, adding the woman’s behaviour drew attention even before she had boarded the flight at LAX airport.
“It was weird, something like you see on TV. You never expect to think you’d be on that same flight.”
Southwest Airlines said in a statement that the pilot chose to divert to Corpus Christi, Texas, after crew members reported “a potential threat in the cabin”.
Henrietta Mokwuah, who was also aboard the flight, told the network that the woman came close to opening the emergency door located near the rear of the plane.
“Oh yeah, she tore off a piece of it. There was the frame, that was on the door. She ended up breaking it off,” Ms Mokwuah said.
The woman refused to stay in her seat and made remarks about being treated unfairly by the government as she paced in the aisles, passengers say.
Cleveland Independent School District Police identified the off-duty officer who detained the woman as Pamela Minchew, who had joined the police force only two weeks earlier.
Officer Minchew had been on holiday with her children, and was returning home to Texas, according to Police Chief Rex Evans.
Due to differences in air pressure, experts say it would be almost impossible for a passenger to open the door of an aircraft during a flight. Added to that, the doors are locked during flight.