Authorities are calling Rowley "a person of interest" because they are not certain Rowley fired the shots, just that the SUV is registered to him.
"We're hoping he's somewhere in the Book Cliffs because that's where we're concentrating" the search, said Uintah County Undersheriff John Laursen.
Laursen said deputies have "had some issues in the past" with Rowley, but Laursen declined to elaborate. He also said Rowley had worked as a control officer with the U.S. Department of Agriculture in Nevada several years ago.
"We do know that he is an avid gun collector and he loves shooting," Laursen added.
A search of Utah court records shows Rowley was convicted in 2009 of a misdemeanor counts of possessing a weapon while under the influence and driving under the influence. He was sentenced to 12 months probation.
The shooting occurred just before 9 p.m. Thursday, as the deputy was investigating a report of a suspicious vehicle near State Road 45 and the Book Cliffs, about 10 miles south of Vernal, according to Laursen.
The deputy pulled over Rowley's 1999 white Chevy Suburban in the Red Wash Road area. While talking to the man the deputy smelled alcohol on his breath. The man then drove away and a short chase ensued. Rowley stopped on SR 45 near mile marker 20, Laursen said.
"This time he decided to shoot at the officer," Laursen said.
The deputy did not fire any shots before the man fled again.
Laursen said the officer's "fast reflexes" are what "saved his life."
Police believe the deputy was going about 15 miles per hour when he approached the SUV. When the deputy sensed danger, he put the truck in reverse and lay down in the seat while driving backward.
The three bullet holes in the truck's windshield, driver's seat and headrest indicate "he would be dead if he stayed where he was," Laursen said.
Since the shooting, police have been inundated with leads and tips, but none have been fruitful. The man's relatives also are helping police. "Friends and family of the man are being very cooperative because they are just as perplexed as we are," Laursen said.
Laursen said about 30 personnel from the various local police agencies, as well as the FBI, were searching on the Utah side of the border, while Colorado personnel were searching three counties in their state. Rangers from Dinosaur National Monument also joined the search. The UHP sent its helicopter to aid searchers, said UHP Cpl. Todd Johnson. An undisclosed amount of airplanes also were searching Friday.
Laursen said there are cabins and oil rigs in the area where Rowley could take shelter, or he could be holed up in his Suburban in any number of canyons and alcoves in the vast Book Cliffs area.
The search will continue for the man throughout the night and won't stop until police find him or have exhausted every avenue, Laursen said.
The Suburban has Utah plate Z936PB.
Anyone who has seen the vehicle or has information is asked to call Uintah County dispatch at 435-789-4222.
Authorities, however, request that no one approach Rowley, who is described as "extremely dangerous and unpredictable."