Newport Beach police’s mounted unit has added a fourth steed.

Police Officer Shawn Dugan, who works for the unit, had been in the market for a new partner after his horse Levi was put down with severe health problems in July.

Dugan looked at about 10 over several months, but none suited his needs. When he met an 8-year-old quarter horse in Lake Perris last month, he knew his search was over.

Dugan named him Bullseye after Woody’s toy horse in the “Toy Story” sequels.

“I have little kids at home that love ‘Toy Story,’ ” he said.

Bullseye performed well when introduced to man-made items like tarps and flags that a police horse would see in a typical day but could startle many horses.

The better the horses respond, the easier it will likely be to train them before they hit the streets, according to Dugan.

Before Bullseye started his law enforcement career, his previous job was ponying thoroughbred racehorses off the track.

Standing at 15.3 hands (a unit of measurement applied to horses that approximates the width of a human hand), Bullseye is a big horse.

But he has a calm demeanor, which makes him an ideal candidate for a job in the mounted unit, Dugan said.

“I couldn’t be happier,” Dugan said. “Finding the right partner is everything.”

hannah.fry@latimes.com

Twitter: @HannahFryTCN