They have no "atheist" beliefs, in the special sense you have given us to understand that you use the word.
They just don't have gods, in the sense that differentiates gods from natural entities and/or storytelling beings of various kinds.
But even a quick and cursory Google turns up a lot of stuff like this: http://www.darkfiber.com/atheisms/atheisms/dine.html or this, if you have academic access: http://www.pep-web.org/document.php?id=joap.025.0208a
This discussion of the colonial imposition of concepts from Western Civilization on other people has a lot of content piled up over the years, and the Navajo religion has played a disproportionately large role - for one thing, it's still here. It wasn't wiped out by the great epidemics and subsequent Abrahamic colonization of North America.
It's not as ugly any more, true. But I think it would serve.
I came across a strange [to me] idea that the Navajo religion is not theism because they don't worship the Yeis, their deities.
According to general internet sites, for example:
Navajo gods and other supernatural powers are many and varied. Most important among them are a group of anthropomorphic deities, and especially Changing Woman or Spider Woman, the consort of the Sun God, and her twin sons, the Monster Slayers. Other supernatural powers include animal, bird, and reptile spirits, and natural phenomena or wind, weather, light and darkness, celestial bodies, and monsters. There is a special class of deities, the Yei, who can be summoned by masked dancers to be present when major ceremonies are in progress. Most of the Navajo deities can be either beneficial or harmful to the Earth Surface People, depending on their caprice or on how they are approached. Navajo mythology is enormously rich and poetically expressive. According to basic cosmological belief, all of existence is divided between the Holy People (supernaturals) and the Earth Surface People. The Holy People passed through a succession of underworlds, each of which was destroyed by a flood, until they arrived in the present world. Here they created First Man and First Woman, the ancestors of all the Earth Surface People. The Holy People gave to the Earth Surface People all the practical and ritual knowledge necessary for their survival in this world and then moved away to dwell in other realms above the earth. However, they remain keenly interested in the day-to-day doings of the Earth Surface People, and constant attention to ceremonies and taboos is required in order to keep in harmony with them. The condition of hozoji, or being in harmony with the supernatural powers, is the single most important ideal sought by the Navajo people.
http://www.everyculture.com/North-America/Navajo-Religion-and-Expressive-Culture.html
According to iceaura, this is a misrepresentation of the Navajo beliefs by theists.
I only know what is available on the web about the Navajo. Could someone clarify for me how theism is defined? Is the Navajo society an atheistic society?