No one but a deeply disturbed individual marches into an elementary school or a movie theater and guns down random, innocent people.

That hard fact drives the public longing for a mental health system that produces clear warning signals and can somehow stop the violence. And it is now fueling a surge in legislative activity, in Washington and New York.

“Anytime you have one of these tragic cases like Newtown, it’s going to expose deficiencies in the mental health system, and provide some opportunity for reform,” said Richard J. Bonnie, a professor of public policy at the University of Virginia’s law school who led a state commission that overhauled policies after the 2007 Virginia Tech shootings that left 33 people dead. “But you have to be very careful not to overreact.”

New York state legislators Tuesday passed a gun bill that would require therapists to report to the authorities any client thought to be “likely to engage in” violent behavior; under the law, the police would confiscate any weapons the person had.

And in Washington, lawmakers said that President Barack Obama was considering a range of actions as part of a plan to reduce gun violence, including more sharing of records among mental health and law enforcement agencies.

The White House plan to make use of mental health data was still taking shape late Tuesday. But several ideas being discussed — including the reporting provision in the New York gun law — are deeply contentious and transcend political differences.

Some advocates favored the reporting provision as having the potential to prevent a massacre. Among them was D.J. Jaffe, founder of the Mental Illness Policy Org., which pushes for more aggressive treatment policies. Some mass killers “were seen by mental health professionals who did not have to report their illness or that they were becoming dangerous and they went on to kill,” he said.

Yet many patient advocates and therapists strongly disagreed, saying it would intrude into the doctor-patient relationship in a way that could dissuade troubled people from speaking their minds, and complicate the many judgment calls therapists already have to make.

One fundamental problem with looking for “warning signs” is that it’s 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 Michael Stone, a New York forensic psychiatrist who has a database of 200 mass and serial killers.

“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,” 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 don’t qualify for any diagnosis, experts said.

Some experts, like Paul Appelbaum, director of the Division of Law, Ethics and Psychiatry at Columbia University’s medical school, says Newtown is an opportunity to re-envision mental health care, focus on vigilance for problems in young people and reduce stigma.