A study found 43 percent of people executed between 2000 and 2015 had been diagnosed with a mental illness at some point.

Upset that people with schizophrenia and other mental disorders have been put to death after murder convictions, lawmakers in a handful of states want to bar the use of the death penalty for people with a serious mental illness.

People accused of murder who are found not guilty by reason of insanity can serve time in a mental hospital and avoid the death penalty. But many states have a narrow legal definition of insanity — not knowing what one did was wrong. And critics say that leaves many people with mental disorders to be found guilty of capital crimes and sentenced to death.

Some of them have already been put to death. Ohio executed a man with schizophrenia in 2001. Arkansas did the same in 2004. A schizophrenic Texas man spent two decades on death row after his insanity plea was rejected, leading to a 2007 Supreme Court ruling that inmates must have a rational understanding of their punishment before they can be executed. (The state continued to seek his execution until a lower court halted it in 2014.)

Legislators in at least seven states — Arkansas, Indiana, Ohio, South Dakota, Tennessee, Texas, and Virginia — have proposed bills this year to prohibit the death penalty for people who suffered from a serious mental illness at the time of their crime. Most of the proposals name specific disorders, including schizophrenia, bipolar disorder, major depressive disorder, delusional disorder, and post-traumatic stress disorder.

Research by academics and the American Civil Liberties Union suggests many people on death row have a mental illness. A study from a professor at the University of North Carolina found that 43 percent of people executed between 2000 and 2015 had been diagnosed with a mental illness at some point in their lives, although not all were serious enough to be covered by the proposed legislation.

Backers of the proposals say that because of the way these diseases affect people’s thinking and impulses, they are less culpable and ought to be spared from the most severe punishment allowed under law, just as children and the intellectually disabled are. The concept is backed by the American Bar Association.

“If these people aren’t seeing the world for what it truly is, if they can’t concentrate and think things through, if they’re so delusional or depressed their thinking isn’t reality-based anymore, they should not be held to the same standard,” said Megan Testa, a psychiatrist who helped draft the list of disorders included in the Ohio bill.

But opponents, including many prosecutors, say the legislation is unnecessary, because people with a serious mental illness are already protected by pretrial competency reviews and can plead not guilty by reason of insanity.

They also disagree with the requirement in many of the proposals that prosecutors prove a defendant had not been suffering from a severe mental illness at the time of the crime, saying the burden should fall instead to the defense to prove a defendant was mentally ill. Because some of the bills don’t specify how severe a disorder must be, opponents also worry the defense would be used too widely.

In many states, the bills are being discussed as part of a broader debate about the death penalty. Ohio has paused executions amid a lawsuit stemming from a botched execution in 2014. Arkansas is set to carry out eight executions by the end of this month, when its supply of fatal drugs expires, after struggling to find enough witnesses to sit in on the process.

Public support for the death penalty has been falling since the 1990s, and a 2002 poll found 75 percent of Americans opposed the death penalty for the mentally ill.

“We do have a legal death penalty in Ohio for a certain class of crimes, and I support that,” said Republican state Sen. John Eklund, who sponsored the bill there. “But defending that punishment will become increasingly difficult if the punishment is not administered and adjudicated in a humane and responsible way.”