Tucson, Arizona (CNN) -- The suspect in Saturday's shooting at an Arizona supermarket has had some contacts with law enforcement, the Pima County Sheriff's Department's lead investigator said Wednesday, but none so alarming that authorities were concerned about what he might do.
Pima County Sheriff's Bureau Chief Richard Kastigar said that speculation law enforcement had enough information about Jared Loughner to stop the shooting is "completely untrue."
"I couldn't underscore that more," Kastigar told CNN's "John King USA."
"The events that led up to what happened Saturday as they relate to law enforcement contact really do not add up in their totality to anything that would cause a police officer to say. 'This guy is going to go out there and shoot 20 people.' There's nothing there," Kastigar said.
The law enforcement contacts included episodes of underaged drinking and possessing drug paraphernalia, which Kastigar described as "very minor occurrences or interactions with law enforcement." Kastigar also said investigators had found no evidence Loughner followed up on suggestions from Pima College officials that he seek mental health help for behavioral problems.
Six people were killed in the shooting on Saturday and 13 others -- including Rep. Gabrielle Giffords -- were wounded. Giffords, whom police said was the target of the shooting, remains in critical condition but her doctors have been pleased with her progress.
Loughner, 22, appeared in a Phoenix federal courtroom Monday to formally hear the charges against him -- including two counts of murder, two counts of attempted murder and one count of attempting to kill a member of Congress. He is now in federal custody.
And on Wednesday, the Ninth Circuit Courts designated a district judge in California to hear Loughner's federal case. Judge Larry Burns is a 2003 Bush appointee serving in the U.S. District Court for Southern California, based in San Diego. The next scheduled federal hearing in the case is January 24 in Phoenix.
All federal judges in Arizona have recused themselves from hearing the case. The chief federal judge in Arizona -- Judge John Roll of Tucson -- was among those killed in the Saturday shooting.
Kastigar said that investigators are looking for a black bag Loughner was carrying early Saturday morning when he had a brief discussion with his father, Randy Loughner, in the Loughners' front yard, Kastigar said.
"The father asked him questions similar to 'What are you doing? What is that?' and Jared mumbled something back to his dad, and his dad said he didn't understand what was said," Kastigar said. "It was unintelligible, and then Jared left."
The elder Loughner got in his vehicle and tried to follow his son, but could not find him, Kastigar said.
Kastigar said that investigators found "a locked box of some kind and within that box was an envelope and a piece of paper and hand-scrawled on those pieces of paper were a few phrases."
"Die cop," "die bitch" and "assassination plans have been made" were among the phrases, he said. One of the pieces of paper found in the box was a letter from Giffords thanking Loughner for attending a 2007 event, he said.
Mark Hart, spokesman for the Arizona Game and Fish Department, said Loughner was stopped by an officer for running a red light at 7:30 a.m. on the day of the shooting. He was given a verbal warning and released.
Kastigar added that investigators are now certain that Loughner acted alone. A "person of interest" they had been seeking identified himself to police. He turned out to be a taxi driver who dropped off the suspect at the shopping center, Kastigar said.
Loughner's parents said Tuesday they do not know why the shooting occurred and that they were "very sorry" for the loss felt by victims' families.
"There are no words that can possibly express how we feel. We wish that there were, so we could make you feel better. We don't understand why this happened," the family said in its statement. "It may not make any difference, but we wish that we could change the heinous events of Saturday. We care very deeply about the victims and their families. We are so very sorry for their loss."
After the shooting, attendees at the Giffords event tackled Loughner and held him down until law enforcement arrived. The Pima County Sheriff's Department said Loughner used a Glock 19 with a magazine that held 31 rounds -- all of which were recovered at the scene.
CNN's Bill Mears contributed to this report