"Rip Van Winkle" is a comic piece. First, it adheres to the broadest sense of the definition of "comedy," which is a work of literature with a happy ending. Rip loses twenty years of his life but in many ways is happier at the end of the story than the beginning, for his wife is dead, his children grown, and his hated adult responsibilities—always his nemesis—are over.

If we define comedy as a funny or laugh-inducing text, "Rip Van Winkle" also qualifies. We are meant to chuckle at the happy-go-lucky Rip's troubles with his shrewish wife, who is a comic type rather than a fully developed character. There's also humor in Rip's confused return to his village after 20 years, including his initial incomprehension that the United States is now an independent country. We are meant to laugh at and with this lovable but ambition-free main character.

The story has, however, a more serious purpose. The chief clue to this is the time period of Rip's long "nap": he bridges a period of profound change in America as it moves from colonial status to independent democracy. Rip represents the old, apathetic, unfocused ways of America when it was under British domain. He is the opposite of the active, involved citizen of the new republic.

Irving is part of generation of writers involved in establishing a national identity for a new country. Irving contributes to this by showing the new vigor brought about by independence compared to the lackadaisical attributes of a character like Rip. This too is a "comic" vision: we are presented with an independence narrative that is a rousing success.

In my opinion, this is clearly a comic piece.  At times, Irving pretends to be serious, but I think this is just one of his ways of making the story more amusing.

Irving pretends to be serious by telling us where the story came from.  He cites his sources, in effect, and seems to be trying to show us that the story is serious.

But most of the story is amusing.  Irving describes Rip and his relationships with others in rather funny ways, for example.  One example of this is

A termagant wife may, therefore, in some respects, be considered a tolerable blessing; and if so, Rip Van Winkle was thrice blessed.

Much of the story revolves around the relationship between Rip and his wife and how henpecked he is and that is generally seen as amusing.