A Swiss woman visiting Washington with a tour group was shot and killed last night by a man who robbed her and two others in the group as they walked near their hotel in Southwest.

An intensive search for the suspect began shortly after the 9:30 p.m. shooting, and police in helicopters, on foot, in cars, and with a dog continued searching during a torrential thunderstorm that briefly deluged the area.

The victim, identified as Mrs. T. Eggimann, of Dornach, a few miles south of Basel, was shot once in the upper left chest, and died less than an hour later in the emergency room of George Washington University hospital.

The shooting occurred shortly after the woman and her two companions had finished dining at their hotel, the Skyline Inn, at 10 I St. SW. They were in the 900 block of Half Street SW, on a brief after-dinner stroll, when they were approached from behind by a man with a gun.

The man attempted to get the women's purses.Exactly what happened next was not immediately, clear. But in a few seconds, Eggimann was shot and the robber was fleeing with three purses.

A homicide detective, noting that none of the three tourists spoke English, said it was possible that their inability to understand the robber may have led to the shooting.

Immediately after Eggimann was shot the other two women ran into the hotel, shouting "polizei!" the German word for police.

One police officer, in a car not far away, hurried to the scene, and, directed by passersby, began a pursuit. Another officer, after hearing a "pop" that sounded like a firecracker, was summoned by neighborhood children who breathlessly took his arm and told him what happened.

Driving nearby, Lucho Young, 21, of Chesapeake, Va., saw a man run in front of his car, carrying three purses. The man ran west through an alley. Young followed him in his car until be climbed a 6-foot wall and, dropping one of the purses, disappeared from view.

Police continued to comb the area late intro the night but as of early today, no arrest had been made.

The 50 persons on the tour, who came from all over Switzerland, had arrived in New York on Tuesday, and after a visit to Philadelphia, came here Friday afternoon.

Robi Williman, the tour leader, said he had advised thye group to avoid the side streets near the hotel at night.

"I told them not to go on the side. . . ." he said.

Williman described the victim as a woman in her 60s who was active and had been enjoying the visit.

He said he was trying early this morning to contact the woman's relatives in Switzerland, but had not yet succeeded.

Members of the tour were scheduled to leave Washington today for Florida.