Although, as I wrote earlier, I don't see film noir as expressly concerned with theological issues, there is a sense in which the idea of "the death of God", as a kind of metaphorical expression for existential bewilderment, gets close to the heart of the tradition.
Edgar G. Ulmer's Detour, a low-budget thriller from 1945, was arguably the first true film noir. It offered a vision of the world as a moral maze from which there was no exit -- an image that accorded well with the unconscious dread which gripped America in the wake of WWII and in the shadow of nuclear apocalypse.
In this light, it's interesting to look at Ulmer's The Black Cat, a strange Universal "horror film" from the early 30s. There, the source of the horror that ensnares its innocent protagonists is a modernistic version of the old dark house -- which sits on the site of a ghastly battle from WWI, somehow infected by the mass slaughter that took place there.
This may not be enough to prove that Ulmer saw a connection between the moral chaos of Detour and the horrors of WWII but it certainly suggests that there may have been an unconscious association of the two ideas in Ulmer's mind.
Certain modern commentators want to see film noir as a phenomenon with essentially political implications -- something that's not hard to argue given the leftist leanings of many of the great masters of the noir tradition, a number of whom were eventually blacklisted. But seeing film noir as essentially political expression I think sells the phenomenon short. Film noir reflected an existential dread far deeper than politics could encompass. "The death of God" gets closer to expressing this than "the corruption of Capitalism".
Curiously enough, the French critic Luc Mollet said that Ulmer's whole body of work expressed "the loneliness of man without God". A recent essay on Jules Dassin's Brute Force, included in Criterion's DVD edition of the film, quotes Mollet dismissively and ironically, suggesting that he was just offering a kind of smokescreen for the political underpinnings of the noir vision. But I think it makes more sense to see the nutty, irrational Stalinism of many noir filmmakers as a smokescreen for the more comprehensive psychic dislocations of post-WWII America, in which Communism and Stalinism were just faddish, ill-conceived replacements for a God who seemed to have abandoned the world in the desert outside Los Alamos, New Mexico, after clearly announcing, at places like Auschwitz, his plans to retire permanently from the world's affairs.
If film noir were simply a reflection of the politics of its leftward-leaning makers, it ought to be terribly dated today, after the demystification of Communism and Stalin, those ephemeral shibboleths for which the Hollywood radicals martyred themselves. But film noir still speaks to us as strongly as it ever did -- perhaps because "the loneliness of man without God" still troubles the spirit, while the passing of Stalin and Communism go conspicuously unlamented.
[Thanks again to Tony D'Ambra of films noir whose posts on film noir and the death of God prompted the thoughts above -- and to Michael Mills' classic film blog for the Detour advertising art.]