Tonka the police horse kept her poise patrolling the real Occupy Washington. But the Morgan cross bucked when confronted Sunday by a small model of the protest encampment set up on an obstacle course.

Officer Megan Lau of the Maryland National Capital Park Police couldn’t explain her horse’s reluctance, which cost her points during the 29th annual North American Police Equestrian Championships in Gaithersburg.

“Maybe she’s having flashbacks to the real Occupy,” Lau said. “She did just fine here until the tents.”

More than 70 police officers from mounted units from as far away as Kentucky and Ontario competed on the sod course at the Montgomery County Agricultural Fairgrounds, which was designed around replicas of Washington’s landmarks and other urban sights and sounds — steam billowing from a street grate, the air brakes of a Metrobus.

Horses had to push their way through giant beanbags painted with the faces of the presidents from Mount Rushmore, into a miniature reflecting pool, around a turnstile at a faux Washington Monument and past water spraying from a fountain at a model of the World War II Memorial.

The course was designed to distract horses with bright colors and sudden, loud noises.

Lt. Stacey Collins of the U.S. Park Police, its designer, explained to participants that the competition was more like police work than Olympic dressage. “You are walking through a beat,” she said, with emphasis on the word walking, as opposed to trotting or cantering.

Cops who ride horses have been doing this competition for nearly three decades as a way to showcase their skill at calming and maneuvering large animals to safely disperse unruly crowds, chase drug dealers and stay still amid chaos, even though a horse’s first instinct is to flee danger and avoid precarious situations.

Horses that have performed well under stress on the street were not all enamored with the obstacle course, even though judges went to extremes to ease fears. Several mounts didn’t flinch when two cardboard Secret Service agents — or, more properly, Men in Black — with menacing weapons popped up on the course in front of a model White House. But they veered wildly at the billowing steam and the Metrobus brakes.

Course officials played Mozart over a loudspeaker to soothe an excitable horse from Boston named Mystic before she began her exercise (Mystic is a classical music lover). But that didn’t stop the horse from throwing her rider, Park Ranger Gene Survillo, head-first into the dirt at a point on the obstacle course where Survillo had to reach down to move an object meant to simulate a traffic cone. Survillo’s plight prompted an urgent alert over the loudspeaker — “Loose horse! Loose horse!” — as Mystic sprinted away.

Police from big cities took home the prizes: Officers from the Toronto Police Service claimed first and second place, and a park ranger from Boston took third.

While it seemed the layout favored horses more accustomed to policing urban streets than rural trails, neither horses from big cities or ones from small towns wanted anything to do with the steam grate or the bus. Both are obstacles encountered every day in any city, but Lau pointed out that “we don’t usually ride inches from a bus. You know how bus drivers drive.”

Lau’s usual beat is the 36,000 acres of parks in Montgomery County, but she and Tonka often find themselves in downtown Silver Spring, and they helped the U.S. Park Police with the Occupy patrols.

Where Jacqueline Copeland volunteers for the 40-member sheriff’s department in Wyoming County, in Upstate New York, there is no Occupy and no street grates. She rides through hundreds of square miles of farmland boasting 100,000 cows, the biggest town just a bit more populated than the county’s famous prison, Attica.

Copeland’s Mr. Te wasn’t fazed by the protest camp, but he didn’t know what to make of the bus, bolting to the side as the brakes sounded. He refused to cross over the steam grate.

“We have to work on that,” said Copeland, making plans to train with smoke bombs to get ready for next year.

The Baltimore Police Department sent four horses to the competition, three years after nearly losing its 123-year-old mounted unit, one of the oldest in the country, to budget cuts.

Private donors gave $90,000 in 2009 to keep city cops on horses. And 7-Eleven helped out with a check for $5,000, but the donation came with naming rights. So Blackie became Slurpee, the name the Percheron competed under Sunday.

Like other horses, the one named after the frozen beverage, and the only horse with a corporate sponsor, had trouble with the bus and its hissing brakes. “That’s unusual for him,” said his rider, Officer Christopher Tran. “We go by buses all the time.”

But unlike Tonka, Slurpee walked by the Occupy obstacle without hesitating. “We were down there enough,” he said, referring to the protest group that camped at Baltimore’s Inner Harbor.