The long delays in the Garner investigation, which has been especially closely watched, have come about for several reasons: There are inherent complexities in the federal civil rights law and a desire among officials to move with caution in a delicate matter. But there has also been, according to those involved, a heated disagreement over how — and even whether — to go forward. Prosecutors with the United States attorney’s office in Brooklyn, whose jurisdiction also extends to Staten Island, Queens and Long Island, have expressed doubts that they can prove in court that a crime had been committed; their counterparts in Washington have claimed that they are confident they have sufficient evidence to proceed.

The dispute came to a head at a recent meeting in Washington, where both offices offered their opinions to Attorney General Loretta E. Lynch. Ms. Lynch, formerly the top federal prosecutor in Brooklyn, must now decide between siding with her former colleagues or with the special civil rights team that investigates such cases. It is unclear both what and when she will decide.

“It is taking quite a bit of time,” said William Yeomans, a fellow at the American University School of Law, who once served as the acting assistant attorney general for civil rights. “I’d almost say it’s been longer than expected, especially since a video exists.”

That video, which, by now, has been viewed around the world, showed Mr. Garner, 43, struggling in the grasp of Officer Daniel Pantaleo, who was trying to arrest him on suspicion of selling loose cigarettes on a Staten Island street in July 2014. Five months later, a state grand jury declined to bring charges against Officer Pantaleo, touching off a wave of protests in New York and a national debate about policing in minority communities.