I've written about this before, but I have observed that patients who believe in God aren't afraid to die as they know life will not end. These patients tend to be happy all the way to the end. On the other hand, patients who don't believe tend to face death with "benign resignation." They tend to be unhappy and depressed.
Those who believe are filled with hope, and, for the most part, they tend to be your patients who are filled with joy and the anticipation that what was promised will be fulfilled. Those who do not believe think that life will just end. Since they believe there is no future for their spirit, they have no hope, and therefore no joy.
Of course there are exceptions to this rule, but for the most part this is what I observe. As you get into discussions with your patients, or as you observe the objects they bring with them (Bibles, crosses, books, etc.), you can get a good picture as to who is a believer and who is not. The believer who knows he's going to die may be sad, yet he won't drag you down with him. In his room you may find books, such as the Bible.
You will see that these patients, since they know it's not the end, will continue to nourish their minds with knowledge, both fictional and nonfictional. They know that what they learn in this life will be useful in the next. Yet those who do not believe will, for the most part, tend to shut down any attempt to learn.
So as you make your rounds the next time you work, you should be able to easily see which of your patients are believers and which are nonbelievers.