Arrests constitute only one measure of involvement, of course. The police are asked to find people with dementia who wander and to bring them home. They stop in for safety checks when family or doctors worry about elders’ welfare.

Especially when people have dementia, “they may be disrupting a neighborhood or engaging aggressively with someone they don’t know, and the police end up being called,” Dr. Williams said. Nursing home staff members, too, may call 911 when they feel unable to handle belligerent patients.

Such interactions can be helpful — or they can go very wrong. For Mr. King, a civil rights lawyer, it’s clear which category his mother’s detention fell into. “This was such a profound breakdown of procedure and good sense,” he said.

The acting police chief disagreed, saying last summer that the officers had acted within department policy and state law, and had “a duty and obligation to take action to protect the other residents from assaultive behavior.”

Mr. King has filed a complaint with the San Francisco Police Department’s accountability division, accusing officers of excessive force, unlawful detention and violations of disability law.

Yet Mr. King recognizes that “as bad as it was, it could have been a lot worse,” he said.

And that’s certainly true. In other high-profile cases last year:

■ A county sheriff’s deputy in Minneapolis, Kan., used a Taser on a 91-year-old nursing home resident with Alzheimer’s who refused to get into a car for a doctor’s visit.

■ After a 65-year-old in San Jose, Calif., was arrested and charged with trespassing, a judge — informed that the man had Alzheimer’s — dismissed the charge. But deputies at the jail released him before a friend arrived to pick him up, and he wandered onto a highway, was hit by a car and killed.