Unfortunately, I didn't love it. The idea is clever - a tenant in an apartment building is murdered, and we're given the testimony of other people in the building (or neighborhood). It's never made clear who the people are talking to - we presume the police - but it is made clear that it's recorded dialogue, as they occasionally acquire new pieces of information while talking. So it's a murder mystery and a "slice of life" book. Fabulous. Except it's not, really.
I think the best way to describe it is that it comes across very much as a novel written by a grad student - there are lots of nice ideas, but very little subtlety. Yes, there are some sly, and quite fabulous, literary allusions (though you probably need to be a serious lit dork to pick up on some of them), but the novel also wears its politics on its sleeve, and it gets grating after awhile. The characters are caricatures. The fact that they all know each other and talk about each other doesn't create a sense of intertwined lives - it just seems repetitive. At first, the various misunderstandings between people are kind of interesting and cute, but they rapidly become predictable, usually because the author can't resist using the same trick again.
So while it's meant to be this thoughtful consideration of immigrant life in Italy - which is a really worthwhile topic, and one that deserves more attention, and especially, more literary description (Roddy Doyle does a good job of it, I think, in The Deportees and Other Stories), this book doesn't quite live up to its promise.