The 40-year-old man was responsible for provoking a traffic accident around 10.30am at the entrance to the motorway in Saint Maurice, travelling west toward Lausanne, cantonal police said in a release.
He drove his vehicle into the rear of a car driven by a woman, according to the release.
The man got out of his car and began conversing with the woman and then suddenly jumped into the woman's car and drove off with it, police said.
The woman, who was not injured, contacted emergency services to report her car had been stolen.
Police at around 11.15am received reports that the man was behaving in a strange way outside the Saint Sigismond church, where he was taking off his clothes.
He entered the church and climbed up to the organ loft, from where he jumped to the ground, six metres below.
He died on the spot, police said.
Investigators did not release further information about the victim.