An unemployed D.C. man on probation for a 1981 burglary was arrested last night in the slaying Sunday of an 18-year-old woman who was fatally stabbed along with her mother in their Northwest apartment.

Police said the suspect, Joseph E. Dailey, 25, of 2143 Suitland Terr. SE, was taken into custody after he appeared voluntarily at police headquarters accompanied by his father.

Homicide detectives said Dailey had been charged in a D.C. Superior Court arrest warrant with second-degree murder in the killing of Sharon Johnson, whose body was found in an alley behind a supermarket in the 3400 block of 14th Street NW shortly after midnight Monday. Investigators said she had been stabbed numerous times in the upper torso.

About two hours after the body was found, detectives went to the victim's apartment about a block away at 1455 Oak St. NW, where they discovered the body of Jean Johnson, 48, the slain girl's mother, on the living room floor. Police said Jean Johnson, a cleaning woman at George Washington University Hospital, had also been stabbed repeatedly, apparently with a carving knife found in the apartment.

Police said they believe that both women were stabbed during a violent quarrel in the apartment sometime Sunday evening, and that Sharon Johnson fled to escape their attacker but collapsed in the alley before she could find help.

The two women and Sharon Johnson's 3-year-old daughter, Natasha, had moved from Southeast into the federally subsidized, 50-unit Oak Street Apartments only a week earlier, according to neighbors. Police said they found the child asleep and unharmed in a bedroom after the slayings.

Dailey, whom investigators described as Sharon Johnson's longtime boyfriend, is on probation after being convicted in a Prince George's County court of a burglary last year in the 3800 block of Southern Avenue. He was being held without bond last night in the central cellblock pending arraignment today in Superior Court.

Police investigators said they expect to present evidence against him to a grand jury in the death of Jean Johnson.