In this classic short story by Edgar Allan Poe, the falling action starts with the man's dismembering the old man's body and burying it under the floor boards and continues through the arrival and questioning by the investigators and his imagining being able to hear the still beating heart of the man he killed. Falling action is typically the event or series of events that immediately follow the climax and lead to the ultimate resolution of the story. In this case, the resolution is the man spilling out the truth that he is the murderer. He is driven to this final reveal by his guilt over his what he has done.
I disagree with the above interpretation. Since the climax of a story is typically thought of as the moment of the most tension, I would locate the climax in the second to last and last paragraphs of "The Tell-Tale Heart," when the narrator's growing anxiety, fear, and, perhaps, guilt, seem to be getting the best of him, and he confesses to the crime.
Unlike the moment when he actually kills the old man, a moment not particularly tension-filled, the narrator's certainty that the police officers are aware of his guilt renders the penultimate paragraph particularly tense. He thinks that he hears the beating of the (dead) old man's heart beneath the floorboards, and he is sure that the officers hear it too. In just these paragraphs, the narrator uses twenty-five exclamation points to convey his tension. However, if the climax -- the narrator's belief that he can hear the dead man's heart and that the police know, and the narrator's eventual confession to the murder -- arrives in the final lines of the story, this means that the story actually has no falling action; it concludes with the climactic confession of the narrator and we are left to imagine what takes place afterward.