Isabella County Sheriff Leo Mioduszewski said the man was identified as Eric Ramsey, 30, of Mount Pleasant.
"We don't know what possessed him to do that. We may never find out," Mioduszewski said.
The woman was abducted Wednesday from the campus in Mount Pleasant, about 120 miles northwest of Detroit. The sheriff said Ramsey drove the woman in her own vehicle to a home off campus and bound and raped her there.
He said Ramsey then put her back in the Ford Escape and pledged to kill her, but she escaped the moving vehicle and ran to a home yelling for help.
While the woman was inside the home talking to an emergency dispatcher on the phone, Ramsey "ended up pouring gasoline on the house and then lit on fire," Mioduszewski said in a statement.
A 14-year-old boy, his 11-year-old sister and 2-year-old brother were alone inside the home in nearby Lincoln Township when the woman banged on the door for help. The teenager, James Persyn III, told Mlive.com that he let the woman in, locked the door and grabbed his hunting knife.
He said he while the woman was using his phone to call 911, he moved her, his siblings and the family dog into the bathroom.
Meanwhile, the sheriff said, "one of the homeowners arrived home ... and was able to put the fire out," using an extinguisher.
Ramsey was spotted early Thursday in Otsego County, where he rammed the first of two state police cars. The sheriff said he subsequently stole a garbage truck and was fatally shot by a deputy in Crawford County, about 70 miles north of the university.
Campus police Chief Bill Yeagley said Ramsey told the woman that he chose her at random outside the Student Activity Center on campus. The chief said the woman saved her own life by fleeing from the car.
"I believe she made all the right choices," Yeagley said. "She's the true hero in this."
Central Michigan University President George Ross said the school would support the Grand Rapids-area woman and her family.
Ramsey had been on parole since last summer after serving the minimum five-year prison sentence for assault with intent to do great bodily harm, according to Corrections Department online records. The maximum sentence was 15 years. Inmates are eligible for a parole review once they serve the minimum punishment.
"The parole board generally doesn't give a rationale for why or why they don't parole (an inmate)," said Russ Marlan, a Corrections Department spokesman. "I looked at his behavior in prison. He was pretty good. He had six misconducts over five years. That's a small amount. He was in minimum security the entire time."
Ramsey had a job, regularly met with his parole officer and had tested negative for drugs, Marlan said.
His record also included convictions for destruction of police or fire property, resisting police and assault with a dangerous weapon.