The F.B.I. investigation, however, painted a murkier picture. Mr. Wilson told investigators that Mr. Brown had tussled with him through the window of his police car and tried to grab his gun, an account supported by bruises and DNA evidence. Two shots were fired during that struggle.

Image Attorney General Eric H. Holder Jr. will make a final decision with his civil rights chief, Vanita Gupta, in the officer’s case. Credit... David Goldman/Associated Press

What happened next, as the confrontation moved into the street, is in dispute. While some witnesses were adamant that Mr. Brown had his hands up, some recanted their stories. Mr. Wilson testified that Mr. Brown had charged at him, and other witnesses backed up his account.

“I’m backpedaling pretty good because I know if he reaches me, he’ll kill me,” Mr. Wilson told a state grand jury, in testimony that investigators said was consistent with what he told the F.B.I. “And he had started to lean forward as he got that close, like he was going to just tackle me, just go right through me.”

Mr. Holder said that the Justice Department’s investigation into Mr. Brown’s death would be independent from the one conducted by the local authorities. While the F.B.I. and local officials conducted some interviews together and shared evidence, the analysis and decision-making were separate. Mr. Holder resisted calls from local officials to announce his conclusion alongside the county prosecutor last year, in part because he did not want it to appear as if they had reached their decisions together.

Federal investigators interviewed more than 200 people and analyzed cellphone audio and video, the law enforcement officials said. Officer Wilson’s gun, clothing and other evidence were analyzed at the F.B.I.’s laboratory in Quantico, Va. Though the local authorities and Mr. Brown’s family conducted autopsies, Mr. Holder ordered a separate autopsy, which was conducted by pathologists from the Armed Forces Medical Examiner’s office at Dover Air Force Base in Delaware, the officials said.

The federal investigation did not uncover any facts that differed significantly from the evidence made public by the authorities in Missouri late last year, the law enforcement officials said. To bring federal civil rights charges, the Justice Department would have needed to prove that Officer Wilson had intended to violate Mr. Brown’s rights when he opened fire, and that he had done so willfully — meaning he knew that it was wrong to fire but did so anyway.