The Supreme Court on Tuesday threw out the standards Texas used to decide that a convicted murderer was not intellectually disabled and thus eligible for execution, continuing a trend of the justices narrowing how states can make such determinations.

The court decided 15 years ago in Atkins v. Virginia that executing what it referred to as the “mentally retarded” violated the Constitution’s prohibition against cruel and unusual punishment. That decision generally left it up to the states to set the standards for such designations.

But in 2014, the court stuck down Florida’s guidelines as too rigid. And on Tuesday, Justice Ruth Bader Ginsburg said that the process Texas uses creates “an unacceptable risk that persons with intellectual disability will be executed.”

In a 5-to-3 decision written by Ginsburg, the court sent back the case of Bobby James Moore, who fatally shot store clerk James McCardle in a botched robbery in 1980. Moore’s decades-long trip through the appeals courts has been marked by conflicting opinions on whether he is intellectually disabled.

Texas’s Court of Criminal Appeals eventually determined that he was not. But the Supreme Court concluded that this decision improperly relied on outdated medical standards, borderline IQ scores and a list of unique-to-Texas factors that Ginsburg termed an “invention . . . untied to any acknowledged source.”

[High court reviews Texas standards for determining intellectual disability]

“Texas cannot satisfactorily explain why it applies current medical standards for diagnosing intellectual disability in other contexts, yet clings to superseded standards when an individual’s life is at stake,” Ginsburg wrote. She was joined by Justices Anthony M. Kennedy, Stephen G. Breyer, Sonia Sotomayor and Elena Kagan.

Chief Justice John G. Roberts Jr. dissented from the decision, along with Justice Clarence Thomas and Samuel A. Alito Jr.

Roberts said the majority “crafts a constitutional holding based solely on what it deems to be medical consensus about intellectual disability. But clinicians, not judges, should determine clinical standards; and judges, not clinicians, should determine the content of the Eighth Amendment,” which forbids cruel and unusual punishment.

Moore’s attorney at the Supreme Court, Washington lawyer Cliff Sloan, said the ruling contained a lesson for states. “The Supreme Court has made clear that no state may assess intellectual disability in a manner that would allow for the execution of someone who has intellectual disability under current medical standards,” Sloan said in a statement.

It was the second time this term that the Supreme Court has ruled for a Texas death-row inmate. Last month, the court ruled that Duane Buck’s death sentence was infected by racial prejudice because of testimony that he might pose a future risk because he is black.

[Court says race-based testimony discriminated against black inmate]

In Moore’s case, Ginsburg said the Texas court followed the “accepted, uncontroversial” process for determining intellectual disability: whether the subject had low IQ test scores, an inability to learn basic skills and adapt behavior to changing circumstances, and whether these deficits began when the person was a minor.

But she said the Texas court was too rigid in relying on Moore’s IQ results, which were slightly higher than 70, generally considered a dividing line. Scores are imperfect, she said, as the court had found in the 2014 Florida case.

[Supreme Court strikes down Florida law on mentally impaired inmates]

Ginsburg noted Moore’s deficiencies — that at 13 he had trouble understanding the days of the week, that he failed every class before dropping out of school, that he had lived on the streets as a teenager.

The Texas court had seen Moore’s survival as a test of his adaptive strengths. He played pool for money and mowed lawns. The Texas court and Roberts in his dissent noted that Moore provided the firearms for the robbery, that he wore a disguise and that he fled to Louisiana to escape capture.

After a Texas judge, following years of court proceedings, found Moore intellectually disabled, the Court of Criminal Appeals overruled. It said the lower court should have used the 1992 standards contained in a decision it issued on determining such disability, not on current standards.

The Moore case has drawn attention because of Texas’s use of additional standards to judge a person’s adaptive behavior, another way of saying whether a person can go about daily life as others would.

A Texas judge likened the factors to the “Lennie” standard, a reference to Lennie Small, the gentle but deadly fictional farmhand in John Steinbeck’s “Of Mice and Men.”

The judge wrote that most Texas citizens might agree that Lennie should be exempt from execution because of his lack of reasoning skills but that other killers might not be exempt.

Ginsburg did not mention the Lennie standard but said the Texas factors “are an outlier, in comparison both to other states’ handling of intellectual-disability pleas and to Texas’ own practices in other contexts.”

Roberts and the dissenters agreed with the majority’s concern about one of the specific factors used by Texas, saying that the adaptive-behavior standards “are an unacceptable method of enforcing” the court’s decision in Atkins.

The case is Moore v. Texas.