Arriaga is accused of killing Newman police officer Ronil Singh - who, like him, was an immigrant.
Christianson explained that Arriaga illegally crossed the border into Arizona "some time ago".
Christianson didn't say when the 33-year-old came to the USA but said that the Mexico native has been living here for several years.
Gustavo Perez Arriaga, 32, was arrested in connection with murder of Newman, CA Police Officer Ronil Singh. Christianson added that Arriaga has a criminal history of driving under the influence and was a member of the Sereno street gang.
He was shot a few minutes after radioing that he was pulling over a grey pickup truck that had no license plate in Newman, a town of about 10,000 people, officials said. "He's not coming back".
At a press conference Thursday, a reporter asked Stanislaus Sheriff Adam Christianson what would happen to K9 Sam after her handler's death.
"Build the Wall!" he wrote as the partial government shutdown, precipitated by an unwillingness of Republicans and Democrats to compromise on a spending bill to include the president's demand for $5 billion to fund a border wall.
Cpl. Ronal Singh, who came to the US from his native Fiji, was shot early Wednesday after stopping the man he suspected of driving drunk in Newman.
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A press conference is being held at the Stanislaus County Sheriff's Department on Friday at noon to talk about "significant developments" in the case.
A suspect was arrested in the killing of a California police officer, police said Friday.
On Thursday, meanwhile, authorities announced that the suspect is an illegal immigrant in the U.S.
Christianson said the two men "intentionally lied to us, tried to divert us, they misled us, they provided informartion that was false, all in an attempt to protect their brother".
Trump tweeted about Singh's killing Thursday, saying it was "time to get tough on Border Security".
Officer Singh was a native of Fiji and has been employed by Newman Police Department since July 2011.
Other officers discovered Singh shot and took him to a nearby hospital, where he was later pronounced dead. "He came to America with one goal, and that was to serve this country".
Newman's police chief said the department and its 12 sworn officers were grieving. The Stanislaus County Sheriff's Department shared that their son was 5 months old.
Singh, the department's first officer to die in the line of duty, drove more than two hours each way to attend the police academy in Yuba City, Richardson said. He called Singh an "American patriot".