CHAMBLEE, Ga. — Witnesses to the fatal police shooting of an African-American man gave differing accounts Tuesday. But they all ended with a similar question: Why was it necessary to shoot Anthony Hill, a 27-year-old Air Force veteran who was naked and unarmed?

The shooting, which occurred early Monday afternoon, has prompted mourning, confusion and anger in the apartment complex northeast of Atlanta where Mr. Hill lived.

“He was a calm, friendly person,” said Julio Hernandez, 54, a groundskeeper at the complex whose 14-year-old son rode skateboards with Mr. Hill. “To me, this was police abuse, because what can a naked person do?”

On his social media accounts, Mr. Hill, an aspiring musician, hinted that he had a mental illness. And most everyone who saw him at the apartments Monday said his behavior was bizarre in the extreme in the moments before the police arrived. Mr. Hill, they said, had been lying on the ground, semi-clothed and then naked, and had been jumping repeatedly off his second-story balcony.