There have always been questions among scholars about Hume's personal religious views. Now, it's true that in conversations with friends, Hume's attitudes seemed more ambiguous and nuanced, but in his writings, he gave every appearance of being an atheist. He was highly critical of Christianity as an institution, for one thing. His analysis of religious belief suggested that religious belief was by nature unreliable. He argued that religious miracles, as violations of the laws of nature, were extremely unlikely.
But his most extensive treatment of religion was found in his posthumous book, Dialogues Concerning Natural Religion. Here, Hume took on and systematically dismantled many of the central arguments that tried to prove God's existence, especially the argument from design. Now, it's true that this book is written in the form of a dialogue, so some scholars have wondered whether the main skeptical character is really to be identified with Hume, and whether all this character's arguments are supposed to be accepted.
Others think that this is a classic case of scholars working too hard to find things to be perplexed about. Hume wanted the book published posthumously. 'Nuff said?
In any case, Hume's reputation as an atheist had very real consequences in his personal life. He was accused by some of his contemporaries of being an "enemy of religion." One of them, William Jones, went so far as to claim that Hume's sole purpose in life was "to invent a sort of philosophy that should effect the overthrow of Christianity." Hume was convinced that his reputation was the main reason he was denied the academic posts for which he applied. Just goes to show you that politics in academia ain't nothin' new.