Prosecutors sought the death penalty in the case.
The Ohio Public Defender's office, which represents Arnold, said the case contains important constitutional questions about double jeopardy because she received her life without parole sentence only after the jury deadlocked on the question of capital punishment.
Arnold's lawyers wanted the supreme court to reverse the 2nd District Court of Appeals decision and send the case back to the trial court for re-sentencing. The Ohio Supreme Court, without comment, declined.
Baby Paris died Aug. 30, 2008. A Montgomery County grand jury indicted Arnold on one count of aggravated murder in December 2006. But on Jan. 28, 2008, the judge in the case declared a mistrial.
Arnold was found guilty in the second trial in August 2008 and was sentenced to life without parole. That conviction was overturned on appeal in November 2010.
Arnold went on trial a third time in April 2011 and was found guilty and sentenced to life without parole. In December 2013, the 2nd District Court of Appeals affirmed the conviction.
"This defendant was found guilty by 24 jurors during two separate jury trials," Montgomery County Prosecutor Mat Heck Jr. said in a written statement. "With today's decision by the Ohio Supreme Court declining to accept her final appeal, we hope that, finally, this horrifying case is closed and the defendant will serve the rest of her life in prison for murdering her own 28-day-old baby girl in a microwave oven."
Arnold's attorney, Stephen Hardwick, could not be reached for comment.
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