On Sunday, the San Bernardino County Sheriff's Department said it had scaled back the search. Los Angeles Mayor Antonio Villaraigosa announced a $1 million reward for information leading to Dorner's arrest and conviction, spurring hundreds of tips.

The trail picked up again on Tuesday, when Karen and Jim Reynolds came upon a man who looked like Dorner in their house across the street from the sheriff's command center in the Big Bear area. He tied them up and took off in their purple Nissan, according to police.

The unit had been unoccupied since January 29 and they had last done some work on it on February 6, Karen Reynolds told reporters.

They returned on Tuesday to continue working on the apartment, she said. "We had come into the living room and he opened the door and came out at us," she said.

"He yelled, 'Stay calm,'" Jim Reynolds said. "When he jumped out and hollered, 'Stay calm!' Karen screamed and turned and started running and he ran after her and he caught her on the staircase and brought her back."

Dorner tried to calm them, the couple said. "He had his gun drawn the whole time," Karen Reynolds said.

He ordered them to lie down and bound their hands behind their backs with plastic ties, telling them he would not kill them, but needed transportation out of Big Bear, they said.

He then gagged them, put pillowcases on their heads and left, they said.

Throughout, he was calm, they said.

"He said I don't have a problem with you, I just want to clear my name," Jim Reynolds said.

The man then took their 2011 Nissan Rogue, they said.

It was not clear how long he had been there, a bag of carrots and milk were in the refrigerator, they said.

At around 12:20 p.m., some 15 minutes after he left, they freed themselves and called 911 to report the incident, they said.

"We're very happy to be alive," Karen Reynolds said. "I didn't wish him dead though ... I prayed for him a lot and I'm praying for his family now."

A 'guy with a big gun'

At 12:45 p.m., Fish and Wildlife wardens spotted the SUV and began pursuing it.

The wardens, driving in separate vehicles, chased Dorner, and a gunbattle ensued. One of the warden's cars was hit, and Dorner crashed his car and ran, according to authorities. He then carjacked a pickup truck.

Rick Heltebrake, a camp ranger, said he was driving when he saw the crashed purple vehicle -- and then something terrifying.

"Here comes this guy with a big gun, and I knew who it was right away," Heltebrake told CNN affiliate KTLA. "He just came out of the snow at me with his gun at my head. He said, 'I don't want to hurt you. Just get out of the car and start walking.' "

Heltebrake said the man let him take his dog and walk away with his hands up.