A 24-year-old man and a 19-year-old woman who shared an apartment in Falls Church were found shot to death there last night, apparently of self-inflicted wounds, city police officials said. A spokesman for Falls Church police said they were investigating the deaths as an apparent double suicide, pending a determination by the medical examiners' office.

Lt. Gregory D. King said the two shootings apparently occurred within minutes of each other, and that police learned of the first one about 8 p.m. when a woman telephoned to say that her boyfriend had just shot himself in the head and asked them to come to a second-floor apartment at the Westbrook Garden Apartments in the 900 block of Ellison Street.

King said police in the area were dispatched in "less than a minute," and that as two officers were on the stairway leading to the apartment, they heard a gunshot from inside. The officers kicked down the door and found the man and woman lying unconscious in the bedroom. Both had been shot in the head, and a .38 calibre pistol was found nearby.

Police said the man was taken to Fairfax Hospital and the woman to the shock-trauma unit of the Washington Hospital Center. Both were pronounced dead shortly after arrival.

Police declined to identify either victim early today pending notification of their families. Neighbors said the couple had shared the one-bedroom apartment since about mid-summer.

King was unable to provide a motive for the shootings, but other police officers and neighbors of the couple said the man had recently lost his job.

"He had just told me he had been laid off a couple of days ago," said neighbor Marilyn Robison.

"I'm a manager at a dairy store across the way and he was over there this afternoon about 2:30," Robison said. "He was the same . . . just joking and kidding around," said Robison. "Then him and her came in around at 3:30 or 4 and they were kidding around and carrying on with each other. It's pretty hard to believe this happened."