People familiar with the case said the federal probe has also been complicated by two witnesses who recanted their statements as the investigation progressed. One was a woman who said she saw Mr. Brown with his hands up in the air when he was shot, according to one person familiar with the case. She later told authorities she had not seen that herself, but was recounting what someone else had told her, this person said.

At his news conference announcing the grand jury decision on Monday, St. Louis County Prosecuting Attorney Bob McCullough said some witnesses “admitted that they didn’t witness the event at all but merely repeated what they heard in the neighborhood or assumed had happened.’’

Mr. Bagenstos said he was hopeful that a separate Justice Department investigation into the police culture in Ferguson, Mo. would yield positive results.