WASHINGTON — Twelve years after barring execution of the mentally disabled, the Supreme Court on Tuesday prohibited states in borderline cases from relying only on intelligence test scores to determine whether a death row inmate is eligible to be executed.

In a 5-4 decision that split the court’s liberal and conservative justices, the court said that Florida and a handful of other states must look beyond IQ scores when inmates test in the range of 70 to 75. IQ tests have a margin of error, and those inmates whose scores fall within the margin must be allowed to present other evidence of mental disability, Justice Anthony Kennedy said in his majority opinion.

A score of 70 is widely accepted as a marker of mental disability, but medical professionals say people who score as high as 75 can be considered intellectually disabled because of the test’s margin of error.

In 2002, the court said that executing mentally disabled inmates violates the Eighth Amendment prohibition on cruel and unusual punishment. But until Tuesday, the justices left to the states the determination of who is mentally disabled.

Kennedy said the finality of capital punishment requires giving inmates the chance to present evidence of mental disability in borderline cases.

“The states are laboratories for experimentation, but those experiments may not deny the basic dignity the Constitution protects,” Kennedy said in an opinion that was joined by the court’s four more liberal justices.

At most, eight other states employ a similar cutoff of 70, Kennedy said. He listed those states as: Alabama, Arizona, Delaware, Kansas, Kentucky, North Carolina, Virginia and Washington. Kansas has not executed anyone in nearly 50 years and Washington recently suspended its death penalty, he said.

In dissent for the four justices to the right of Kennedy, Justice Samuel Alito said the court has no evidence that relying on test scores just above 70 is unreasonable and so should not be held unconstitutional.

Tuesday’s decision came in the case of 68-year-old Freddie Lee Hall. Lawyers for Hall said there is ample evidence to show that he is mentally disabled, even though most of his multiple IQ tests have yielded scores topping 70. Hall has been on death row for more than 35 years since being convicted of murdering a pregnant 21-year-old woman in 1978. In nine tests administered between 1968 and 2008, Hall scored as low as 60 and as high as 80, with his most recent scores between 69 and 74, according to the state.

A judge in an earlier phase of the case concluded Hall “had been mentally retarded his entire life.” Psychiatrists and other medical professionals who examined him said he is mentally disabled.

As far back as the 1950s, Hall was considered “mentally retarded” – then the commonly accepted term for mental disability – according to school records submitted to the Supreme Court.