A few caveats:
1) There's actually an umlaut in the title, but I don't know how to format umlauts in Blogger. Yes, I'm aware that there's also an umlaut in "umlaut" that I can't type, either.
2) This is not the first Esther Diamond novel. If you decide to pick up this book based on my recommendation, you should probably not pick up this book. You should pick up Disappearing Nightly, which is the first book but which is not listed as the first book in this book because the series started under another publisher and the publishers of this book were apparently not about to give free publicity to a book they were hoping would go out of print so they could buy the rights and get the whole series under the same publisher. So although there's a handy info-dump at the beginning to get you up to speed, you probably don't want to do what I did and buy this book thinking it was the first book.
3) Full disclosure: Laura Resnick, author of Dopplegangsters, first came to my attention by making lots of smart, insightful, level-headed comments on the whole Puppy mess on File 770, and by posting cute pictures of her foster kittens on Facebook. I freely admit that I will pick up your first novel based on your cute cat pictures. After that, you need to have talent.
And with those caveats out of the way, let's talk Dopplegangsters. The first thing I'll say is that the book cover does a good job of setting expectations. The title, the cover art and the back cover copy all suggest a screwball comedy paranormal romance-mystery about Esther Diamond, an out-of-work actress who's waiting tables at a Mafia restaurant and bumps into a gangster twice in one night...only to witness his gruesome murder the next night. It turns out (spoilers!) that mob enforcers all over town are sprouting magical twins, and dying horrifically not long afterwards.
With those expectations in mind, the book lived up to them very nicely. Esther is a charming, sympathetic character with a good head on her shoulders and enough determination and smarts to make her a believable solver of bizarre gangland paranormal slayings, but she's also human and relatable enough to make her a believable out-of-work actress who's in way over her head a lot of the time and coping with the situation using wry humor and the occasional bout of panic.
Max, her sorcerer friend, is a bit caricatured--you'll recognize him from a lot of urban fantasy stories who have powerful immortal magic-wielders that are a bit out of touch with the modern world. But he's a well-done take on the caricature, and has some genuinely funny moments. Lopez, Esther's cop boyfriend who isn't particularly thrilled at her involvement with the Mafia, is sympathetic despite having a lot of plot functions that should theoretically force him to be a jerk (he's the token skeptic, he's trying to sideline Esther for her own safety, and as a cop he starts to get more than a little suspicious that Esther is hanging around with gangsters all the time). In some ways, he's the best character.
But really, the show is repeatedly stolen by good-guy hitman "Lucky", whose basic response to finding out that magic is real and that a professional killer is using it to whack people is, "Okay, that sucks. We should find that guy and kill him." There are a lot of great gags involving Lucky's pragmatic approach to the mystical world, and the impromptu education he provides Esther and Max in moving through his own territory without getting killed.
The mystery itself isn't exactly complicated--there's really only about three suspects, and Resnick takes the Agatha Christie tack of "the person who seems least likely to have done it is the obvious suspect". But this isn't really about the mystery--it's about the people solving it, and Resnick does an excellent job of creating characters that you want to spend time with. It's a book you don't so much read as hang out in, and the charming atmosphere will definitely make you want to spend a little more time with Esther Diamond.