Romell Brown, who raped and murdered a teenager in 1984, argued a second execution attempt was a “cruel and unusual punishment”. Broom was convicted in 1984 of raping and killing Tryna Middleton, a 14-year-old girl who was abducted in Cleveland as she walked home from a football game with two friends.
Earlier this year, Ohio’s Supreme Court also ruled that Broom should face the death chamber a second time.
Broom, now 60 years old, is only the second inmate to survive an execution in US history.
In 1947, Louisiana electrocuted 18-year-old Willie Francis by electric chair – a year after an improperly prepared electric chair malfunctioned.
The death penalty is a divisive issue for US Supreme Court judges.
In Broom’s case, two liberal justices said they would have granted his appeal had they not been outvoted, because they believed the execution attempt had taken place under “especially cruel and unusual circumstances”.
The US Supreme Court also rejected the appeals by three other convicted murderers: Henry Sireci in Florida, James Tyler in Louisiana, and Sammie Stokes in South Carolina.
No new execution date for Broom has been set, and it could be several years before another attempt is made.
In 2014, Ohio voted to put a moratorium on the death penalty after European pharmaceutical companies refused to supply the drugs used for lethal injections.
Two months ago, the state announced it plans to resume executions in January with a controversial new cocktail which some critics claim is inappropriate.