The first scene of Accidental Death of an Anarchist introduces the Maniac, a certified madman with an "acting mania." Bertozzo, a police officer, interviews the Maniac about his latest charge of impersonating a psychiatrist. The Maniac denies any wrongdoing, revealing his quick wit in his responses. When Bertozzo leaves, the Maniac reenters the empty room and looks through Bertozzo's files. The Inspector from the fourth floor calls, looking for Bertozzo; we can infer that a judge is coming to the station to reopen the inquiry about the death of the anarchist. The Maniac pretends Bertozzo is in the room making rude comments about the Inspector and his situation, prompting the Inspector to later punch Bertozzo in the face. Meanwhile, the Maniac decides to impersonate the judge and conduct the inquiry himself.
In the second scene, the Maniac interviews the Inspector and the Superintendent, asking them to recreate what happened the night of the anarchist's death. They told the anarchist they had proof he had planted bombs at the railway station, that his comrade had confessed to planting a bomb at the bank, and that the anarchist's alibi had collapsed. None of these things were actually true. To demonstrate the effects of such "psychological warfare," the Maniac tells the policemen that there is evidence that they were both negligent and that their careers are ruined. He encourages them to jump out the window, as the anarchist had supposedly done, and they both later admit that they seriously considered doing so.
The Maniac admits his deception and offers to help the policemen make their story more coherent. In their second version of events, the anarchist didn't jump until four hours after the interrogation, allowing the men to claim their lies could not have been what caused the anarchist to commit suicide. The Maniac invents details that support this story: the Superintendent put a hand on the anarchist's shoulder, the Inspector pat him on the cheek and told him not to lose heart, and they all sang a song. The policemen object to the fictions, but the Maniac argues that the public would love such a story and they agree to play along.
At the beginning of Act Two, the Maniac says they need to determine what could have happened between 8pm and midnight to cause the anarchist to jump out the window. Instead, however, he points out a number of inconsistencies in the policemen's testimony: the window was open, yet it was midnight in December when the temperature was below zero; the anarchist would have had trouble reaching the window without a running start or a leg-up; and if the constable had really tried to stop him and held onto a shoe, as he said, then the anarchist must have either had three feet or been wearing two shoes on one foot, since witnesses reported he had both shoes on when he landed on the pavement.
The Journalist arrives and the Maniac says he will take on the disguise of the Captain from Forensics to prevent the Journalist from learning that the inquiry has been reopened. His costume includes an eyepatch, a glass eye, and a wooden hand and leg. The journalist brings up additional incriminating evidence against the police. Why did the previous inquiry omit the report on the trajectory taken by the anarchist's body, which would have established whether or not he was alive when he went through the window? Why was an ambulance called for five minutes before the "jump"? Why, too, were there bruises on the back of the dead man's neck? The Maniac explains that there has been a version of events floating around that says that a few minutes before midnight, one of the interrogators lost control of himself and gave the anarchist a whack on the neck. The whack half paralyzed the anarchist, so they called an ambulance. In the meantime, they opened the window and two policemen leaned the anarchist out, hoping the cold air would revive him. However, they accidentally dropped him, each man thinking the other was holding on. The Journalist says the story would explain a lot, including the reason the prosecutor stated the death should be classified as an "accidental death" rather than a suicide. She and the Maniac also discuss the "unreliability" of the witnesses who confirmed the anarchist's alibi.
The play gears up for its climax with the reappearance of Bertozzo, who has brought a copy of the bomb that exploded in the bank. Bertozzo is acquainted with the real Forensics Captain and knows that the Maniac is an imposter. Eventually, he realizes that he is the madman he had been interviewing at the start of the play. The other policemen, thinking Bertozzo will reveal that the Maniac is a judge, kick him and engage in other slapstick humor to try to keep him silent. Bertozzo, meanwhile, tries to dismantle the Maniac's disguise, revealing that there is no reason for the eyepatch or the false leg.
During this time the Journalist continues her questioning, and it comes out that the bomb was very complex - likely the work of the military. She points out that two of the ten members of the anarchist group were spies and asks how the group could have pulled off such an operation while being kept under close scrutiny. The Maniac agrees that the police would have been better off pursuing fascist or paramilitary organizations rather than ragtag anarchist groups. He tells her his beliefs about scandals - they make the public think that the authorities are doing something, but in reality, nothing changes.
The pace quickens as the Maniac switches his disguise to that of Bishop. Bertozzo tries more frantically to reveal the Maniac's identity, and the Inspector and the Superintendent try more frantically to prevent him. Finally, Bertozzo whips out a gun and threatens to shoot. He has the constable handcuff the others to a horizontal bar and orders the Maniac to confess who he really is. The Maniac shares his files and the others are outraged. He grabs the bomb and tells Bertozzo to drop the gun or he will press the detonator and kill them all. When Bertozzo complies, the Maniac reveals a tape recording of their conversations, which he plans to copy and distribute to political entities and the media.
Suddenly the lights go out and the bomb goes off in the courtyard below. When the lights come back on, the Maniac is gone; we can infer he has jumped out the window and fallen to his death. Since neither the journalist nor the handcuffed policemen had anything to do with the Maniac jumping, the Journalist says she may have to rethink her position about the anarchist's jump. She leaves and the policemen take keys out of their pockets and unlock their handcuffs.
There is a knock on the door and the actor who played the Maniac enters. The policemen surround him, thinking he is the Maniac. However, it turns out he is the actual High Court Judge, there to reopen the inquiry into the death of the anarchist.
Note - this ending appears in Simon Nye's translation. Other adaptations feature different endings, including one where the Journalist must decide between saving the evidence or the handcuffed police officers before the bomb detonates. Please see the section on Challenges of Translation for more information.