Richey has been on death row in Ohio since 1987
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Prosecutors have lodged an appeal in the US Supreme Court against the decision to overturn the murder conviction of a Scot on death row.
In their petition, they argue that the Sixth Circuit Court of Appeals exceeded its powers in the case of Kenny Richey.
Richey was sentenced to death in Ohio in 1987 for murdering a two-year-old girl in a fire.
Prosecutors say he is guilty of murder regardless of who he set out to kill, and they want the conviction upheld.
Richey's conviction was overturned in April by the Sixth Circuit Court of Appeal and prosecutors were given 90 days to release or retry him. Last month, the authorities in Putnam County said he would face a retrial.
In his writ to the Supreme Court, Ohio attorney general Jim Petro said the Sixth Circuit "improperly rejected" the Ohio Supreme Court's reading of Ohio law.
The Sixth Circuit concluded that in order to sustain the murder conviction, the state must show that Richey intended to kill two-year-old Cynthia Collins when he set the fire.
It was insufficient for the state to show that he started the blaze in the hope of killing his ex-girlfriend but instead killed the girl, the writ claimed.
'Proper bounds'
In earlier proceedings in the case, the Ohio Supreme Court ruled it did not matter whether or not he intended to murder the child.
If he meant to kill his girlfriend, but another innocent victim died, that still constituted murder.
Mr Petro said that in rejecting this reading of Ohio law, the Sixth Circuit had "exceeded the proper bounds of habeas".
Cynthia Collins, the child who died in the fire
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The writ also disputed the Sixth Circuit's view that Richey, 40, had ineffective legal counsel during his trial.
"We hope the court will accept review of this important case to provide some measure of justice to Cynthia Collins' family," Mr Petro said.
His Boston-based lawyer has described as minimal the chances of the state securing a conviction a second time round.