Does belief in an afterlife play a role in suicide rates? Religious beliefs, in particular views on the afterlife, could plausibly influence suicide.

Is there some study which tries to look at how belief systems play a role in the number of suicides in some country or in the world?
I think, from a statistical point of view, this question will be impossible to answer, because belief in an afterlife is almost always tied to powerful confounding factors, such as participation in a community of fellow believers, marital status, age, etc. I imagine that religious affiliation probably can have a strong protective effect regarding suicide - though I don't have any statistics to back that up - but I can't envisage how you would separate out the various components of religious affiliation and prove which component(s) made the crucial difference.

You might have heard of Émile Durkheim's famous book Suicide. (Forgive me if I'm assuming either too little or too much knowledge on your part.) Durkheim looked specifically at the effect of religious affiliation on suicide: he found that Jews in late nineteenth century France had the lowest rate of suicide, Protestants the highest, and Roman Catholics somewhere in the middle. Durkheim, however, attributed these findings to the fact that Jews tended to form very tight-knit communities, and that Protestants tended to be much more individualistic, than to any doctrinal difference.

On a more personal note, as a believer who has been through two episodes of severe depression, I think that, broadly speaking, belief in an afterlife probably does have a protective effect with regard to suicide - although there are plenty of factors whose effect is more potent. I have no background in academic psychology, so my advice is probably both unwelcome and unsound, but, if this is part of a formal research project, a good place to start would be to interview believers who had gone through, or were going through, an episode of severe depression. Also, John Donne's Biathanatos provides a very left-field exploration of Christian attitudes to suicide.