This Sunday marks the 24th anniversary of Robert Eugene Carter's death in the District of Columbia's electric chair.On April 26, 1957, Carter, an unemployed construction worker convicted of murder during a $54 robbery, became the last of 106 persons to die by court order in the Nation's Capital since the Civil War.

The argument for a death penalty in the District is about to be replayed all over again, just weeks after D.C. Mayor Marion Barry signed into law the bill formally striking the death penalty from the city's books.

Now, in the wake of the assassination attempt on President Reagan last month, Sen. Strom Thurmond (R-S.C.) has introduced a bill that would reinstate the death penalty for first-degree murder here.

Thurmond, perhaps more than anyone, embodies the worst nightmares of many people in this overwhelmingly black and Democratic city. Nothing dramatized the transition of power brought on by last November's electoral landslide more clearly than Sen. Edward M. Kennedy (d-Mass.), the quintessential liberal, turning over the gravel of the Senate Judiciary Committee to former Dixiecrat and reformed segregationist Thurmond.

Thurmond's bill would allow a jury or judge to decide -- in a separate, second hearing taking into account all the specifics of each case -- whether to impose the death penalty in first-degree murder cases. The approach has withstood various court challenges.

Currently, sentences for first-degree murder convictions range from a mandatory 20-years up to life imprisonment.

Thurmond's bill is particularly sensitive, coming at a time of rising crimes, especially violent and gun-related crimes, in the Nation's Capital. Some local officials, reacting to heightened citizen fears, have begun echoing a hard line toward criminals.

The death penalty reflects the ultimate anticrime sentiment. And it is obvious racial overtones. A Gallup poll released last month showed that whites overwhelmingly -- 70 percent to 22 percent -- favored the death penalty in first-degree murder cases, while blacks split about evenly.

Explaining that wide gap, Gallup pollster James Schreiber said, "Obviously, most of those now on death row are black."

As the debate here is played out, that national split indicated by the poll could color the argument over whether the electric chair is a deterent to murder in Washington. The split is reflected in the comments of two community group leaders that were typical of their separate communities.

Joseph W. Carter, who is black, lives in Southeast Washington and heads the D.C. Federation of Civic Association's citywide panel on police protection. He said, "I personally am not in favor of the death penalty. We must be more concerned with restitution for the victims of crime. p

Joe Jeff Goldblatt, the white vice chairman of Advisory Neighborhood Commission 3C in Northwest Washington in Ward 3, said "I personally am for it. I think the death penalty is a deterrent to murder. Maybe it will take that kind of shock to restore some reality to the criminal justice system." Prison, he said, "is a revolving door, and that door ought to be shut."

But even with such anticrime feelings running high, local politicians are confident that the death penalty will never again become reality in the Nation's Capital. They still consider it political suicide to support the death penalty in a city that is overwhelmingly black and, in essence, still liberal.

But blacks, who have long considered themselves the most likely to suffer discrimination under a death penalty, are increasingly becoming the victims of crime -- often violent crimes perpetrated by other blacks. As Everett W. Scott, former president of the Federation of Civic Associations put it, "Blacks in most instances commit crimes against other blacks."

"Something has to be done," said Virginia Matthews, ANC commissioner in the Edgewood neighborhood of Ward 5, a settled, middle-class black community where the crime rate has been spiraling. "The judges are too easy on people. The police arrest them, but the judges turn around and let them out. I don't know" about the death penalty, she said, "but something has to be done."