The rancher, Jack Yantis, was killed in the shootout, authorities said.
Earlier Sunday, a Subaru station wagon struck the bull on a highway just north of Council, a town of roughly 800 people, and Adams County sheriff's deputies responded to the crash.
The injured bull began charging emergency responders as they worked to get the driver and passenger out of the car, according to the Idaho State Police, the agency that is investigating the shooting.
"The bull was very agitated and was aggressive to emergency services, as well as the other cars coming up and down the highway," Adams County Sheriff Ryan Zollman said.
Yantis, the bull's owner, arrived with a rifle just as deputies decided to put down the animal.
There was an altercation, and Yantis and two deputies all fired their weapons, State Police said in a statement.
Yantis died at the scene, and one deputy suffered a minor injury.
The bull also was shot and killed.
Both deputies, whose names have not been released, were placed on paid leave.
"To the best of my knowledge, this is the first officer-involved shooting that Adams County has ever had," Zollman said. "This is going to be a big hit to this community. The gentleman involved, Mr. Yantis, was a well-known cattle rancher around here. It's just a sad deal for everybody involved, for the whole community."
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