WASHINGTON – Sheriff’s Deputy Charles Hurt was on truant patrol when he came across a teenager in a Baton Rouge park on a cool fall morning. The teenager pulled a gun from his jacket, panicked, he said, and shot Hurt dead.

That tragic sequence took place more than a half-century ago, nine days before the Kennedy assassination in 1963. The teenager, Henry Montgomery, is now 69 years old and has been behind bars almost ever since, serving a life sentence. He wants the Supreme Court to give him a chance to get out of prison before he dies.

Three years ago, the justices struck down automatic life sentences with no chance of release for teenage killers. The question for the court in Montgomery’s case, to be argued Tuesday, is whether that decision in Miller v. Alabama should be extended retroactively to Montgomery and hundreds of other inmates whose convictions are final.

In the 5-4 decision in 2012, Justice Elena Kagan wrote for the majority that judges weighing prison terms for young offenders must take into account “the mitigating qualities of youth,” among them immaturity and the failure to understand fully the consequences of their actions.

A win for Montgomery at the Supreme Court would not necessarily lead to his release. But he would be allowed to present evidence about his childhood and family situation, as well as about his rehabilitation during his long imprisonment.

Through legislative action or court rulings, 18 states have allowed inmates like Montgomery to be given new prison sentences or to ask for their release, according to The Sentencing Project. Louisiana is among seven states that have declined to apply the Supreme Court ruling retroactively. The issue is under review in some other state courts and legislatures.

Nine states abolished the sentence outright after the 2012 decision, bringing to 15 the number that prohibit life terms for those under 18, according to the Phillips Black Project, a public interest law group that focuses on the most severe prison sentences. Seven states have no inmates serving such sentences.

Montgomery’s case probably will turn on just how big a deal the court thinks the 2012 decision was. Groundbreaking decisions in criminal law often are applied retroactively. Montgomery’s lawyers say the court’s decision to outlaw automatic life sentences for teenagers, its latest in a string of rulings about how children bear less responsibility than adults for the same crimes, is such a case.

In response, Louisiana argues that the Alabama case should not be viewed as quite that important because the court only declared unconstitutional such sentences where judges lack discretion, and specifically did not forbid judges from sentencing juveniles to life in prison after consideration of individual circumstances.

Montgomery’s case highlights some of the problems that inmate advocates say plague the criminal justice system generally. Montgomery is African-American, and he was tried for killing the white deputy in a time of racial tension and reported cross burnings in Baton Rouge.

The State Times newspaper of Baton Rouge ran a front-page headline after Montgomery’s arrest: “Negro Held in Deputy’s Murder Here.” The story noted that “more than 60 Negroes were detained” in a parish-wide manhunt.

The Louisiana Supreme Court threw out Montgomery’s first conviction because he did not get a fair trial. He was convicted and sentenced to life after a second trial.

Supporters of the life-in-prison sentences counter that the need for finality is important for the legal system and the relatives of the victims. The punishment may be harsh, but it also is just, Louisiana and its allies say. Deputy Hurt had a wife and three young children.

Hurt’s middle child, Becky Wilson, is part of a victims’ group that opposes reopening Montgomery’s case. Wilson described in court papers how her family struggled after her father’s death and how she had a baby while in high school and gave him up for adoption.

A ruling for Montgomery “will force surviving family members to confront their trauma again,” Wilson and other victims told the Supreme Court.

But other victims are supporting Montgomery because they believe they are honoring their dead relatives by “affording a child who has committed murder the opportunity to demonstrate genuine remorse and change.”

For every inmate like Montgomery, who became a boxing coach and worked in the prison’s silkscreen department, the states supporting Louisiana point to people like James Porter, who was 16 when he killed a Michigan mother and her four children. The victims included a 10-year-old boy who was hiding fully clothed in a shower stall when Porter found him and shot him in the temple and face.

Those states also say that reopening these old cases will be time-consuming and difficult because judges will be asked to assess, sometimes decades after the crime, how an inmate’s youth might have affected his behavior.

The Obama administration is supporting Montgomery. It says states could avoid the costs of resentencing inmates by allowing them to be considered for parole.

Harvard Law School professor Charles Ogletree is calling on the justices to consider banning life-without-parole sentences altogether for people who commit even the most heinous crimes before their 18th birthdays.

Ogletree said the court should take note of the rapid change in sentencing laws to rule out life terms for the young.

A decision in Montgomery v. Louisiana, 14-280, is expected by late spring.