There is no question, Fairfax County police said yesterday, that sometime Thursday morning Laurie Jean Green drove from her home in a quiet neighborhood near Mount Vernon to Woodbridge, where she bought a .38-caliber handgun.

The 31-year-old woman then returned home with the gun, investigators said, and sometime that afternoon shot her 2-year-old daughter Aimee twice, then killed herself with a single shot.

What is not clear, officials said yesterday, is why Mrs. Green did it.

Aimee, the only child of Mrs. Green and her husband, Navy Lt. Cmdr. Norman K. Green, 33, was reported in serious but stable condition yesterday at Fairfax Hospital.

"We don't have any idea at this point why she killed herself," said Fairfax County prosecutor Robert F. Horan Jr. "About all we've learned is that they were a nice couple, they played with the child a lot, they were personable and friendly."

"Police will try to make some sense of it," Horan said, "but at this point it doesn't make any sense at all."

Green found his wife dead and his child wounded when he returned home in midafternoon Thursday after phoning home several times and getting no answer.

The shootings astonished residents of the quiet, park-like neighborhood of $150,000 homes where the family had lived since last August.

"I just loved them," said one neighbor, who asked not to be identified. "They were wonderful neighbors. I talked to her over the fence. That precious little baby, so friendly . . . . It just makes me want to cry, you know?"

Marie Smith, who lives down the street from the Green's home at 9008 Greylock St., said the couple was often outside playing with the baby and riding bicycles together. "They just looked so happy," she said.

Neighbors said the only whiff of dissatisfaction from the Green home was Mrs. Green's expressed desire to return to California to live because she didn't like the weather in the East.

They said the Navy had reassigned Green to a California post and the family had sold their house in preparation for the move.

Smith said Mrs. Green and Aimee were scheduled to return there June 12, to be followed a short time later by Lt. Cmdr. Green.