Updated: 12:22 p.m.

Arizona authorities were searching Sunday for a second person in connection with a shooting that critically wounded Rep. Gabrielle Giffords (D-Ariz.) and killed a federal judge and others.

The Pima County Sheriff’s Department distributed a photo early Sunday of a dark-haired white male, approximately 40 to 50 years old, who was last seen wearing blue jeans and a dark blue jacket. Authorities believe he may be associated with a 22-year-old suspect, who has been identified as Jared Lee Loughner and is in custody.

Authorities say Loughner attacked Giffords and bystanders during a “Congress on the Corner” event at a Tucson Safeway grocery store at about 10 a.m. Mountain time, firing a 9 mm Glock semi-automatic pistol into the crowd. The two men may have arrived at the constituent event together, the Arizona Republic reported.

Giffords, 40, was shot once in the head and was rushed to University Medical Center in Tucson. Of at least 18 people injured, six died: U.S. District Judge John Roll; Gabe Zimmerman, a 30-year-old Giffords aide who was recently engaged; Christina Taylor Green, a 9-year-old girl who had just been elected to her school’s student council; Dorothy Morris, 76; Dorwin Stoddard, 76; and Phyllis Scheck, 79. Roll was at the event to greet Giffords after attending morning Mass, the Arizona newspaper reported.

Authorities said they have evidence that makes it clear that Giffords was the intended victim, the newspaper reported.

Authorities also confirmed to the newspaper that a suspicious package was left at Giffords’ Tucson office Saturday and was being investigated.

Giffords’ communications director, C.J. Karamargin, said late Saturday that the Congresswoman remained in critical condition in intensive care and was not fully conscious, the Arizona newspaper reported. Her district director, Ron Barber, who was wounded in the shooting, was “doing very well” and speaking, Karamargin added. There was no update on the condition of Pam Simon, a caseworker for Giffords who was injured.

Mark Kimble, 57, who works in Giffords’ Congressional office, was at the constituent event Saturday but was not injured. He told the Arizona Republic that a bullet entered the top of Giffords’ head and traveled out the back, but it “didn’t cross the centerline of the brain, which is crucial.”

Former U.S. Surgeon General Richard Carmona, a family friend of Giffords’, was cautiously optimistic but told reporters Saturday night that she could need further surgery. “This is a very devastating wound,” Carmona said, the Washington Post reported. “With guarded optimism, I hope that she will survive.”

John Stanton contributed to this report.