Arkansas may retry a man for murder even though jurors in his first trial were unanimous that he was not guilty, the Supreme Court ruled Thursday.

Alex Blueford, who is accused of killing his girlfriend’s 1-year-old son, is not protected by the Constitution’s Double Jeopardy Clause, the court ruled in a 6 to 3 decision.

Because the judge dismissed the jury when it was unable to reach agreement on lesser charges, Blueford was not officially cleared of any of the charges, the majority said, and thus may be retried.

“The jury in this case did not convict Blueford of any offense, but it did not acquit him of any either,” Chief Justice John G. Roberts Jr. wrote.

The decision brought a sharp dissent from Justice Sonia Sotomayor, who was joined by Justices Ruth Bader Ginsburg and Elena Kagan.

“Blueford’s jury had the option to convict him of capital and first-degree murder, but expressly declined to do so,” Sotomayor wrote. “That ought to be the end of the matter.”

The Double Jeopardy Clause is found in the Constitution’s Fifth Amendment and commands that no person shall be “twice put in jeopardy of life or limb” for the same offense.

Blueford was tried for the death of Matthew McFadden Jr., who died in 2007 from head injuries. Arkansas prosecutors said Blueford intentionally caused the boy’s death, while Blueford maintained that he had accidentally knocked the child to the ground.

Blueford was charged with capital murder, although the state waived the death penalty. At trial, the judge instructed jurors that if they had reasonable doubt about whether he was guilty of capital murder, they should next consider the charge of first-degree murder. If they found reasonable doubt about that, they should then consider manslaughter, they were told, and after that, negligent homicide.

The jurors’ final option was to acquit Blueford of all charges.

After a few hours of deliberations, the jury reported that it might not be able to reach a decision. The forewoman told the judge that the jurors were unanimous against capital and first-degree murder, had split 9 to 3 against manslaughter and did not vote on negligent homicide.

The judge sent the jurors back for more deliberations, but half an hour later the forewoman reported no verdict. The court declared a mistrial.

All agree that Blueford can be retried on charges of manslaughter and negligent homicide, but Blueford claimed the murder charges were off the table because a jury had rejected them.

The Supreme Court majority disagreed. “The foreperson’s report was not a final resolution of anything,” Roberts wrote. “The fact that deliberations continued after the report deprives that report of the finality necessary to constitute an acquittal on the murder offenses.”

He was joined by Justices Antonin Scalia, Anthony M. Kennedy, Clarence Thomas, Stephen G. Breyer and Samuel A. Alito Jr.

Sotomayor’s dissent said the ruling weakens the founders’ concerns about allowing the state to bring repeated charges against those it disfavors.

“This case demonstrates that the threat to individual freedom from reprosecutions that favor states and unfairly rescue them from weak cases has not waned with time,” she wrote. “Only this court’s vigilance has.”

The case is Blueford v. Arkansas .