WASHINGTON – The Supreme Court on Thursday limited the Constitution’s protection against double jeopardy in cases involving multiple charges and deadlocked juries.

The 6-3 decision holds that a jury’s unanimous but tentative vote to acquit a defendant on some charges does not count as a verdict.

It came in the case of an Arkansas man who in 2009 was tried for murder and manslaughter in the death of his girlfriend’s 1-year-old baby. The jury voted unanimously against the murder charge, but the foreman said they were “hopelessly deadlocked” on whether he was guilty of manslaughter. The judge declared a mistrial.

Chief Justice John G. Roberts, writing for the court majority, said the constitutional protection against being tried more than once for the same crime did not prevent the man from being retried for murder. Only a “final decision” of the jury and a “formal verdict” triggers the double jeopardy protection. A jury foreman’s report on the deliberations does not count as a verdict, he said.

The ruling means that Alex Blueford can be retried for murder as well as manslaughter and negligent homicide. Prosecutors said Blueford threw the child to the floor. He said the child fell in an accident.

Blueford argued in his appeal to the Supreme Court that the state’s plan to retry him for murder violated his Fifth Amendment protection against being “twice put in jeopardy of life or limb … for the same offense.” He agreed he could be tried again for manslaughter and negligent homicide.

Lawyers involved in the case doubted the ruling would have a broad impact. In most states, trial judges can poll jurors who are having trouble reaching a verdict and issue a partial verdict on those charges where they are unanimous. Once the jury and judge reach a verdict on some charges, a defendant could not be retried for those same offenses.

The trial judge in Blueford’s case could have polled the jurors and issued a partial verdict acquitting him on the murder counts, but he chose to allow the deliberations to continue. Roberts agreed with the state that jurors can change their minds during deliberations.

Justices Antonin Scalia, Anthony M. Kennedy, Clarence Thomas, Stephen G. Breyer and Samuel A. Alito Jr. agreed.

In dissent, Justice Sonia Sotomayor faulted the court for weakening the historic protection against double jeopardy. The rule “unequivocally prohibits a second trial following an acquittal,” and the trial judge in Blueford’s case should have ruled he had been unanimously acquitted on the murder charges, she said.

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