Urban fiction about a female detective who meets a male shape shifting unicorn

I remember it was an e book, advertised with a blue cover and a coffee cup on it.

The book was really really laugh out loud funny, and the female detective had some kind of substance abuse issue. It wasn't a series, which I remember being sad about.

The female detective met the unicorn cause every one was attracted to them, but she initially wasn't which drove the unicorn mad.

I remember vampires being described as smelling bad in it- and being vaguely slow. It had the detective getting roped in to solve supernatural crimes, and magic etc seemed in that world vaguely normal. I read it maybe 3 years ago, but can't find it on My e readers, and golly I want to read it again so badly.