Barely three hours later - in record time, many longtime Vatican observers noted - the Holy See put out a statement that opened, and quickly shut, the case. It claimed that Tornay had killed the couple before turning the gun on himself in what appeared to have been a "fit of madness."
A final report by Vatican investigators presented in February 1999 confirmed the original reconstruction. Traces of cannabis in Tornay's urine and a cyst in his brain discovered during the autopsy were given as possible explanations of why a simmering professional grudge had exploded into a double murder and suicide.
End of story? Hardly. Ten years on, the play "04-05-'98: Massacre in the Vatican," which opened in Rome last week and runs through Saturday, revives the salacious rumors and murky conspiracy theories that have hung over the case.
Why were the Swiss Guards without a leader for months, and why did Estermann get killed the same day he was appointed? Why were the Italian police excluded from the investigation? Then, if Tornay was killed in a fit of madness, why did he calmly write a suicide note?
Those are just a few of the questions that the playwright Fabio Croce poses in a fast-paced whodunit that happens to provide its own frank answer: Because the Vatican was trying to hide the truth, which is that all three were murdered.
The smoking gun never actually finds its way into the hands of a specific culprit, but in concocting his murder theory, Croce thickens the plot with enough twists to make the audience dizzy.
In the play, the three deaths are interwoven with the unresolved disappearance in 1983 of two young girls, one of whom lived in Vatican City; with the sudden, and some say mysterious, death of Pope John Paul I; with the bailout of the IOR, the Vatican bank, when it was in uneasy financial waters; and with secret service agents of various ilk.
For good measure Croce throws in a bitter rivalry between the clerical freemasonry and the Catholic organization Opus Dei. The two groups were supposedly clashing to gain primacy over the pope's security detail.
"The plot might be a little demanding of people who don't know the case," Croce admitted recently after a run-through of the play, which stars three actors who take on several roles. "It is hard to follow. It even makes me a little anxious."
In the past 10 years the Tornay-Estermann murders have inspired several literary undertakings.
Crime and the Vatican make for good copy, said John Follain, a British reporter and the author in 2003 of "City of Secrets," which is about the case.
"There's the fact that the men were among those in charge of protecting the pope, and then all the quaint picture postcard of the Swiss Guards in the public perception. But the main interest, really, is that three people could die under the pope's window," he said.
Croce, who heads Edizioni Libreria Croce, a publishing house that specializes in gay-themed literature, said he wrote the play because he wanted to know what really went on that night.
"I can't stand the distortion of the truth," said Croce, whose version of the Tornay-Estermann crime - involving Stasi spies, defrocked priests, stolen documents and alleged blackmail, for a start - might come across as extravagant to some.
"It's like a film, a movie but it has nothing to do with the truth," said Luc Brossollet, a lawyer who represents Muguette Baudat, Tornay's mother, who has relentlessly challenged the Vatican's account. After repeated requests to the Holy See to investigate the case anew were ignored, she appealed to a Swiss court to reopen the case.
"We tried until the end with the Vatican to have information, an opening or something but we didn't get anything," Brossollet said. "In the end we turned to the Swiss."
The request is pending and a decision on whether a Swiss court has jurisdiction over the matter is expected by the end of the year, said the lawyer.
In 2002, Brossollet and another French lawyer, Jacques Vergès, published "Murdered in the Vatican, May 4 1998," which drew on evidence from an independent autopsy of Tornay in Lausanne as well as the depositions of expert witnesses on behalf of Baudat.
Their book raised a number of issues with the Vatican's investigation. For instance, Tornay's service pistol used 9 millimeter bullets but the exit hole in his skill was smaller; blood was found in Tornay's lungs which is inconsistent with suicide and suggests he was unconscious for some time before he died; the Lausanne autopsy found no evidence of a cyst in his brain; the reputed suicide letter contained mistakes about personal matters and seemed written by an Italian (Tornay spoke French).
Some of those findings have made their way into Croce's script, which blithely skips between actual documents - including official statements from the Holy See - and supposition. In the end, it's easier to suspend belief.
Does Croce worry about being sued (or coming to a bad end because he knows too much)? "The Vatican won't do anything because I am not powerful enough," he said. "They can let me talk my head off. That way, I become just another voice in the crowd, one of many who protest."
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