As a parody of classic pulp-noir tropes, this is a bit of a wild ride. We're pretty much here to be silly about things, so the story isn't particularly important. There is in fact a definite underlying truth to be uncovered, and we do actually have to collect the evidence needed to finger the right suspect; but the process was silly enough that I actually thought, initially, that none of it would matter.
I'm sure there are people for whom this would by a hoot from start to finish, but I must admit that the clowning about began to feel a bit old to me after a while. This is the sort of outrageous comedy that makes it very difficult to connect with the characters on any level, which is fine in very small doses (say, a Monty Python skit) but maybe a little less so in a longer work. Whether Saint City Sinners qualifies as a short skit or a longer work is probably a matter of opinion.
My opinion, anyway, is that this is like a breakfast of maple-glazed bacon and baked beans, all drenched in maple syrup. Yes, there's some meat there at the bottom, but all I can taste is maple syrup. And maybe some people like it that way, but I can feel my jaw clenching up from the sugar overload.