Does the narrator in The Tell-Tale Heart commit the perfect crime?

By seeming to be insane, the narrator convinces the reader that the murder could have been made for something as trivial as the landlord's eye; that the narrator could have cut up and hid the body and that he could have actually heard the sound of a dead heart beating under the floorboards. In other Words, such strange and incredible occurrences were the result of a deranged mind.