Like other police uses of force, confrontations involving people with diminished mental capacity have increasingly been caught on video and turned into national news. In July, officers in Sacramento shot and killed a man who was walking and running in the street, gesticulating wildly, and who refused to obey orders to drop the knife he was holding or to lie down.

Days later, after an autistic man sat in a street in North Miami, Fla., playing with a toy truck the police may have mistaken for a weapon, an officer tried to shoot him — and instead, accidentally shot and wounded the man’s therapist, who had sat down next to him to try to coax him away.

“There are hundreds of thousands of times when officers are helpful, but far too often, people in crisis end up being Tasered, beaten, arrested and even shot, and a lot of families are very scared to call the police, knowing something like that can happen,” said Laura Usher, criminal justice and advocacy manager at the National Alliance on Mental Illness.

“The underlying problem is there aren’t enough crisis services so people turn instead to 911 but there also needs to be a lot more police training.”