Mark R. Loescher, 51, faces charges of aggravated assault with a deadly weapon without intent to kill after the Friday incident.
According to the probable cause statement, authorities responded to a bank in connection to a call about a man, who had pulled a gun on woman after she approached him about his smoking car.
Loescher and his vehicle matched the description given to authorities, the report said.
Authorities pulled the car over, and Loescher told them he was in the CIA, the report said.
"As I was handcuffing him he told that he had jurisdiction over me since he was the director of the CIA," the law enforcement officer wrote in the statement. "While speaking with Loescher I could see that his comments were very off the wall and it did not appear as if he was all there mentally."
Besides being Presley's brother and CIA director, he also said he was half orangutan and that authorities needed to contact the "Fusion Center to check on his monkey blood."
He also said that he was a "g-man," and that he was good friends with "President Bush and has the same attorney," the report said.
A fully loaded magnum revolver and 104 bullets were seized from the car, which was towed. The passenger was released and taken home.
It wasn't immediately known if he had an attorney.