Police said the man broke into the home of Michelle Cox, who had an unlocked back door.
"When I turned around out of my bedroom, there was a young Hispanic guy standing in my hallway," Cox said.
Police said Barnes is a white man standing 5 feet 8 inches tall and weighing 172 pounds.
Cox, a Dallas real estate agent, said the man threatened to kill her and tried to strangle her. She said he put on some of her clothes after nearly two hours, locked her in a bathroom and stole her car.
Barnes, of Amarillo, was being treated at the University of Texas Medical Branch prison medical center for injuries he got during a fight. Barnes, who authorities say has a history of escapes, escaped late Saturday night.
A state prisons spokeswoman said a wall vent in Barnes' room was removed and several blankets were found tied together. Dallas police said investigators believe he escaped from a hospital window.
“This man tied together 40 feet of sheet and put the sheets out of the fifth-floor window and crawled down,” Senior Cpl. Janice Crowther said.
Authorities said they believe Barnes stole a car in Galveston that was found Monday in the parking lot of a Tom Thumb in Oak Cliff a few blocks away from Cox's house on Monday.
Barnes is serving a 35-year sentence for seven burglaries and aggravated assault.
Dallas police said Barnes should be considered armed and dangerous. He is believed to be driving a 2009 white Chrysler PT Cruiser with Texas tag LYS-388.
Anyone with information about his location should call police at 214-744-4444 or 911.