A 32-year-old woman was fatally injured last night when a 65-foot tree on the grounds of the West German Embassy fell across her car as she stopped to let out a passenger in the 4600 block of Reservoir Road NW, D.C. police reported.

Investigating officers said the woman, who was not named until relatives are notified, died at Georgetown University Hospital shortly after the 6:30 p.m. incident.

Detective Patrick M. Urban of the police traffic division, said a second passenger, who had just gotten out of the car to move from a rear seat to the front, " . . . heard the tree crack, he yelled, he bent over, and the tree came crashing down."

Another investigator, Detective Robert Schaar, said the man was the dead woman's fiancee. The man's name was not released, but a hospital spokeswoman said he was treated for back and neck injuries at the hospital and released.

Urban said the dead woman was a native of Vietnam who left that country at the end of the war 10 years ago. He said she was scheduled to graduate soon from Georgetown University's School of Dentistry and had a 12-year-old son.

Investigators said the tree, 36 inches in diameter at the base, broke off 6 1/2 feet from the ground and fell diagonally across the Toyota Corolla, crushing the roof of the car onto the woman. The tree, part of a dense wood on the embassy grounds, and standing about 40 feet from the road, struck only the one vehicle, police said.

Urban said they are classifying the incident as "an act of God."

A neighborhood resident, Elinore O'Hara, said she heard a very loud crash and looked out her window to see the tree across the car. "I couldn't believe my eyes. The car was demolished. It was horrible."

O'Hara said that workmen had been clearing away trees near where the tree fell last night. Officals of the West German Embassy could not be reached for comment.