Is Hannah's suicide part of the falling or rising action?

Excellent question.

In the rising action part of any story, the main characters are working to resolve or make sense the conflict. For this reason, the suicide cannot fall into the rising action category.

Falling action takes place after the story’s Climax, or turning point. During this time in the story, loose ends are being tied up and the characters are headed toward some semblance of resolution. For this reason, Hannah’s suicide cannot be considered a part of the falling action.
Hannah Baker’s suicide is actually the main conflict of the novel, which can also be defined as the inciting incident.
Without conflict, we have no story. Therefore, her suicide, which is revealed to the readers during the exposition (background) part of the story is the inciting incident that becomes the main focal point of the entire novel. Often the introduction of the story’s conflict happens right before the rising action.

The plot line of most stories contains five different parts: introduction (exposition), rising action, climax, falling action, and resolution (conclusion). Typically, the introduction introduces the main characters and the setting (the time and place). The events of the rising action lead up to the climax. The climax is colloquially known as the "point of no return." It, the climax, exists as the most intense point of the text. The events of the falling action are all the result of the climax (meaning they would not necessarily happen if it were not for the climax). The resolution, or conclusion, tends to bring the story to a close and "tie up all loose ends." The resolution is not always present; in some stories, the author leaves the story with more to come. This type of ending usually results in a sequel.
As for Hannah's suicide in Jay Asher’s novel Thirteen Reasons Why, one could argue that her suicide is part of the exposition. One could argue this by stating that Hannah's suicide is the utter beginning of the story. That said, one could also argue that her suicide exists as the climax. All of the events that she tells of in the tapes (rising action) lead up to her taking her life. Without these events happening, Hannah (most likely) would not have decided to commit suicide. The events which follow her suicide would be defined as the falling action. Essentially, the events which lead up to and follow Hannah's suicide define her suicide as the climax of the story.

In Jay Asher’s novel Thirteen Reasons Why, Hannah Baker is a beautiful, seemingly popular teenage girl who dies by suicide, leaving behind a series of audiotapes for the people whom she believes contributed to her downward spiral.
Rising action refers to events in a story that lead up to the climax. Falling action, in contrast, refers to events that occur after the climax.
Since the novel begins with Hannah’s suicide already having happened, one could argue that her suicide is a part of the rising action.
However, I would suggest that it is actually part of the exposition. The exposition refers to facts of the narrative that a reader must know in order to understand what is happening in a story. Since few literary works start from the absolute beginning of a story, exposition is an essential part of the plot. In this novel, the exposition includes the knowledge that Hannah Baker has already killed herself by the time the story actually begins.