The shootings Tuesday about five miles north of the border near Bisbee left one agent dead and another wounded.
Agent Nicholas Ivie and two others had responded to an alarm triggered by a sensor aimed at detecting smugglers and others entering the U.S. illegally. Ivie was shot and killed.
Another agent was shot in the ankle and buttocks but was released from the hospital after surgery. The third agent was uninjured.
Investigators trying to determine whether friendly fire occurred in a shooting involving law enforcement would compare the ballistics of officers' guns with bullet slugs that were either recovered from or passed through an officer's body, said David Klinger, a criminology professor at the University of Missouri at St. Louis and an expert in police shootings.
The officers involved in the case and any known witnesses also would be asked to provide accounts of such a shooting during interviews with investigators. And investigators would try to establish where officers and witnesses were positioned at the time of the shooting, Klinger said.
The Border Patrol couldn't immediately comment on the frequency of friendly fire shootings at the agency, but such incidents appeared to be extremely rare.
Neither George McCubbin, president of the National Border Patrol Council, nor Kent Lundgren, chairman of the National Association of Former Border Patrol Officers, had ever heard of any friendly fire incidents in the Border Patrol.
"I know of absolutely none in the past, and my past goes back to 1968," Lundgren said, citing the year he joined the Border Patrol. "I'm not saying it never happened. I'm just saying I've never heard of it."
McCubbin has served in the Border Patrol since 1985.
Ivie's death marked the first fatal shooting of an agent since a deadly 2010 firefight with Mexican bandits that killed U.S. Border Patrol Agent Brian Terry in December 2010 and spawned congressional probes of a botched government gun-smuggling investigation.
Terry's shooting was later linked to that "Fast and Furious" operation, which allowed people suspected of illegally buying guns for others to walk away from gun shops with weapons, rather than be arrested.
Authorities intended to track the guns into Mexico. Two rifles found at the scene of Terry's shooting were bought by a member of the gun-smuggling ring being investigated. Critics of the operation say any shooting along the border now will raise the specter that those illegal weapons are still being used.
Twenty-six Border Patrol agents have died in the line of duty since 2002.