A man and woman, found dead of gunshot wounds at a North Arlington garden apartment complex Monday night, died in an apparent murder-suicide, police said yesterday. It was the second such incident in the county in the last two weeks.

Arlington police said that they believe that Grover Lee Carter, 42, of Alexandria shot 25-year-old Joyce Ann Badgley who lived in an apartment at 476 N. Thomas St. and then got into his nearby 1972 Plymouth and shot himself.

A revolver was found on the front seat next to Carter, who police said was employed as an auto mechanic in an Alexandria service station. Police said they discovered trhe body of Badgley, who had been shot several times in the chest, sprawled face down on the floor between the kitchen and dining room in her apartment.

Police said that Badgley , a dancer at the Crystal City Restaurant, knew Carter but refused to discuss a possible motive for the shootings which they said occurred shortly after 9 p.m. Monday.

According to police spokesman Tom Bell, neighbors in the massive red brick Buckingham apartment complex, located near the Parkington Shopping Center, called police after hearing loud music and gunshots from Badgley's one-bedroom apartment. Police said neighbors also reported hearing a second series of shots near the building a short time later.