When Rip returns after twenty years and mentions that he was asleep, the townspeople begin to look at each other, winking and tapping their foreheads, indicating that they think Rip has gone crazy. After all, who falls asleep for that long?

This response is common throughout the village as the news spreads. The consensus opinion appears to be that Rip must not be in his right mind.

However, an old man named Peter Vanderdonk confirms Rip's story. He states that it has long been known that the Catskill Mountains are haunted. He says his father once saw men in old fashioned Dutch clothes playing nine pins and making a sound like thunder, just as Rip recounted.

The weight of Peter Vanderdonk's authority seems to put to rest the rumors that Rip has lost his mind. What people privately believe is not divulged. Rip, at the end of the story, goes off to live with his daughter.

To see what Irving has to say, all you have to do is look at the last paragraph of the story.  However, it's still pretty ambiguous.

Irving says that not everyone in the village believes Rip's story.  But thenhe says that they are just pretending not to believe.  Irving also sort of implies that maybe people shouldn't believe it because Rip kept changing the story.

But, on the other hand, he says that all the old-time people in the village know it's true.  They know that there really are supernatural things out there in the woods and hills.

So, Irving says that some don't believe him (maybe) and some do believe him.