Now, however, as the prosecution phase nears and both federal and state courts pursue the case, complications will inevitably appear ? beginning with the vast number of potential witnesses, and further magnified by the sometimes sharply different requirements of the two court systems.

The complications extend to the rules of evidence. Arizona state and federal rules differ significantly on what defense attorneys are entitled to hear before trial, and the federal and state teams could also head toward very different outcomes as well if ? as many legal experts expect ? Jared L. Loughner?s lawyers mount an insanity defense. Arizona, unlike federal law, does not allow a finding of not guilty by reason of insanity. A defendant can only be found guilty, not guilty or guilty but insane.

?This is not a whodunit ? it?s pretty straightforward,? said the Pima County attorney, Barbara LaWall, whose office is expected to file a state criminal case in the coming weeks against Mr. Loughner, 22, on top of the federal charges already filed. ?It?s also very complicated.?

While the systems differ, the facts are clear-cut: Mr. Loughner, the accused gunman, was caught in the act in front of many witnesses; after a brief search for a man who turned out to be an innocent taxi driver, it became clear that there was no conspiracy; records showed that Mr. Loughner bought the gun legally; there were no interstate connections to explore, nor fugitives to hunt down; the suspect?s Internet postings and papers at his home provided a roadmap to his mental state and fixation on his apparent target, Representative Gabrielle Giffords, who was having an event in the shopping center parking lot where the shooting occurred.

There are human entanglements too. Ms. LaWall, in preparing to counter an insanity defense on the state side, said in an interview that she may get help, in a way, from one of the murder victims: John M. Roll, the chief federal judge in Arizona, who had been a supervising prosecutor in the Pima County attorney?s office decades ago, when she joined it as a young prosecutor.

?I learned to defend against the insanity defense from John Roll,? she said.

The disconnect between the relative simplicity of the investigation and its extraordinary importance is also manifested in appearances.

After the attack, President Obama asked the F.B.I. director, Robert S. Mueller III, to fly out to Tucson and personally oversee the effort. He did, and the news conference he gave on Sunday sent a calming message to the public that the government was in control of the matter.

But Mr. Mueller?s role was not to run the investigation. He flew back to Washington on Monday, then returned briefly to Tucson later in the week. And while he attended some briefings in Arizona as the inquiry unfolded, he also spent time visiting victims in the hospital.

Instead, the investigation has been primarily run by Nathan Thomas Gray, the special agent in charge of the F.B.I.?s Phoenix division, who has nearly three decades of law enforcement experience and a long history of important bureau positions. He is being helped by an assistant special agent in charge, Annette Bartlett, who runs the division?s branch office in Tucson.

At the F.B.I. offices here in a sixth-floor suite downtown, people are working at every available space, according to a description provided by two F.B.I. agents, all revolving around a glossy dark brown conference table that agents refer to as the main battle station, seating 18 to 20 people.

Phone lines and computer cables thread the room together, but there are also voluminous stacks of paper, neatly organized, extending to chairs along the walls. A projector illuminating the list of various leads to cover, referred to as the virtual command center, hangs overhead.

Judy Clarke, Mr. Loughner?s lawyer, did not return a phone call or e-mail requests for comment.

Even as the F.B.I. leads the investigation, however, the Pima County Sheriff?s Department, five miles away in a low-rise complex hard between the County Fairgrounds and an industrial park, has become the main source of information about what has actually been uncovered. The discovery of a black bag on Thursday in a Tucson neighborhood by a man walking his dog illuminated the odd trajectory of news, evidence and turf that swirls around the case.

Investigators had been looking for the bag since being told by Mr. Loughner?s father that he had confronted his son about it on Saturday, before the shootings, and Jared Loughner ran into the desert carrying it. The recovery and detail about its contents, 9-millimeter ammunition ? the caliber used in the attack ? was the stuff of a sheriff?s press release. Later in the day a sheriff?s spokesman said the bag had been turned over to the F.B.I., which had not commented about it.