The ruling will affect not only Florida, which has the nation’s second-largest death row after California, but also as many as eight other states by Justice Kennedy’s count, including Alabama and Virginia. They will now be required to take a less mechanical approach to mental disability in capital cases, said Eric M. Freedman, a law professor at Hofstra.

“Death row inmates commonly suffer from multidimensional mental problems,” Mr. Freedman said. “Today’s ruling requires courts to investigate these fully, by looking at the elephant rather than the tail.”

In Tuesday’s decision, Justice Kennedy said that closer supervision of the states was warranted given the nature of the punishment. “The death penalty is the gravest sentence our society may impose,” he wrote. “Persons facing that most severe sanction must have a fair opportunity to show that the Constitution prohibits their execution. Florida’s law contravenes our nation’s commitment to dignity and its duty to teach human decency as the mark of a civilized world.”

The case, Hall v. Florida, No. 12-10882, arose from the 1978 murder of Karol Hurst, who was 21 and seven months pregnant when Freddie L. Hall and an accomplice forced her into her car in a supermarket parking lot. She was found in a wooded area, where she had been beaten, sexually assaulted and shot.

There was significant evidence in school and court records of Mr. Hall’s intellectual disability. Before the Supreme Court’s decision in the Atkins case, a trial judge found that there was “substantial evidence” that Mr. Hall “has been mentally retarded his entire life.”