The New York statute requires doctors and other mental health professionals to report any person who “is likely to engage in conduct that would result in serious harm to self or others.”

Under current ethical guidelines, only involuntary hospitalizations (and direct threats made by patients) are reported to the authorities. These reports then appear on a federal background-check database. The new laws would go further.

“The way I read the new law, it means I have to report voluntary as well as involuntary hospitalizations, as well as many people being treated for suicidal thinking, for instance, as outpatients,” said Dr. Paul S. Appelbaum, director of the Division of Law, Ethics, and Psychiatry at Columbia University’s medical school. “That is a much larger group of people than before, and most of whom will never be a serious threat to anyone.”

One fundamental problem with looking for “warning signs” is that it is more art than science. People with serious mental disorders, while more likely to commit aggressive acts than the average person, account for only about 4 percent of violent crimes over all.

The rate is higher when it comes to rampage or serial killings, closer to 20 percent, according to Dr. Michael Stone, a New York forensic psychiatrist who has a database of about 200 mass and serial killers. He has concluded from the records that about 40 were likely to have had paranoid schizophrenia or severe depression or were psychopathic, meaning they were impulsive and remorseless.

“But most mass murders are done by working-class men who’ve been jilted, fired, or otherwise humiliated — and who then undergo a crisis of rage and get out one of the 300 million guns in our country and do their thing,” Dr. Stone said.

The sort of young, troubled males who seem to psychiatrists most likely to commit school shootings — identified because they have made credible threats — often do not qualify for any diagnosis, experts said. They might have elements of paranoia, of deep resentment, or of narcissism, a grandiose self-regard, that are noticeable but do not add up to any specific “disorder” according to strict criteria.