A federal judge will hear arguments on his request Tuesday.
In a similar case out of Texas, a federal appeals court found the family of another Mexican teen killed by an agent cannot sue in the United States.
In the latest case, the ACLU filed suit in Tucson against agent Lonnie Swartz. It sued on behalf of Araceli Rodriguez, the mother of 16-year-old Jose Antonio Elena Rodriguez.
The teen was in Nogales, Sonora, near the tall, steel fence that divides the United States and Mexico when Swartz shot him from Nogales, Arizona, on Oct. 10, 2012. An autopsy showed Elena Rodriguez was shot about 10 times.
The Border Patrol has said Elena Rodriguez was among a group of people throwing rocks at agents across the border, endangering their lives.
The ACLU says the shooting was another example of border agents using excessive force without consequences. Araceli Rodriguez says her son was walking home from playing basketball with friends and never had a rock or any other weapon.
Swartz has not been charged, and an investigation by the FBI is ongoing. The Border Patrol declined to say whether he is still an agent.
Swartz's attorney, Sean Chapman, did not return a call seeking comment. Chapman has asked U.S. District Court Judge Raner C. Collins to throw out the mother's lawsuit, saying constitutional protections did not extend to her son.
"Even if Agent Swartz's alleged conduct plausibly violated the Fifth Amendment, (Elena Rodriguez) was not entitled to substantive due process because he neither came within the territory of the United States nor developed substantial connections with this country to justify its extraterritorial application," Chapman wrote in his motion to dismiss.
Lee Gelernt, the ACLU attorney presenting arguments Tuesday, said he is hopeful Collins won't put too much weight on the Texas case.
"In our point of view, that case was decided wrongly," Gelernt said.
U.S. Border Patrol agent Jesus Mesa Jr. shot 15-year-old Sergio Adrian Hernandez Guereca in June 2010 near a bridge between El Paso, Texas, and Ciudad Juarez, Chihuahua. Authorities said Mesa was trying to arrest immigrants who had illegally crossed into the country when rock-throwers attacked him. Mesa fired his weapon across the Rio Grande, striking Hernandez Guereca twice.
A three-judge panel of the 5th U.S. Circuit Court of Appeals originally said Hernandez Guereca's family could sue Mesa. But the full court overturned that ruling in April.
The issue of whether constitutional rights protect non-Americans outside the U.S. in relation to border shootings could end up before the U.S. Supreme Court.
The Border Patrol has come under criticism for its use of force at the border, with several lawsuits filed against the agency alleging excessive use of force. The agency has maintained its agents use force only to defend their lives.
"I think what we saw for many years is a rash of shootings and abuse that gave a feeling of impunity because the Justice Department was never taking corrective action, and I think when there's no corrective action taken, the feeling of impunity develops among the ranks, and it probably starts to feel like they can do almost anything," Gelernt said.
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