The beaten body of a young woman, whose legs were bound with a telephone cord, was found yesterday morning in a freight elevator of a high-rise apartment building in the Logan Circle neighborhood, District police and tenants said.

Police arrested Mohamed Grar, 28, a resident of the building. Grar and the woman apparently had an argument, D.C. homicide detective Louis Greene said.

Police would not comment on details of the homicide or on a possible motive, saying the case is under investigation. The victim, who was 20, had been arrested in the past for prostitution, Green said.

Grar was charged with second-degree murder while armed, a felony that carries a maximum penalty of 15 years to life in prison if convicted. He will be arraigned today in D.C. Superior Court.

Police would not release the name of the victim because they said her relatives had not been notified. The woman had lived in the District for at least three years, but was not from the Washington area, police said.

The body was discovered about 7:30 a.m. by a maintenance worker who had opened the elevator door in the lobby of The Eddystone, an eight-story, 95-unit building at 1301 Vermont Ave. NW.

According to tenants, the assailant appeared to have taken the victim from an apartment, then tried to stuff her body down a trash chute. When the body would not fit inside the chute, residents said, the body was dragged to the elevator.

The victim, who did not live in the building, appeared to have been dead for more than a day, according to a police evidence technician.

The woman was severely beaten about the head, police said. An autopsy is to be performed today.