Prosecutors did not watch video of the nonfatal shooting until weeks after charging the wounded man, an official said.

Almost immediately after an immigration agent shot and wounded a Venezuelan immigrant in Minneapolis this winter, the federal government cast the injured man as an attempted murderer and the agent as the victim of a brutal beating.

That version of events began unraveling when prosecutors dropped felony charges against the injured man, Julio C. Sosa-Celis, and one of his housemates, Alfredo A. Aljorna, who had fled from immigration agents.

Yet video footage of the shooting, newly obtained by The New York Times, raises questions about why it took weeks for the government’s case to fall apart.

The video contradicts the agent’s claim that three assailants had beaten him with a shovel and broom for roughly three minutes before he opened fire. Instead, the confrontation depicted in the video lasts about 12 seconds and shows two men struggling with the agent. It shows no sustained attack with a shovel.

The federal government had access to that video within hours of the shooting on Jan. 14, the Minneapolis police chief said. Yet prosecutors did not watch the footage, an official said, until nearly three weeks after they filed charges against the two men.

“Bare due diligence would have shown that the agents were lying,” Mayor Jacob Frey of Minneapolis said in a recent interview, shortly after he watched the video for the first time.