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Has anyone ever heard of Jackaby by William Rittier?
I haven't finished it yet but the back literally says "Doctor Who meets Sherlock," and so far, it definitely fits that... A narcissistic, trench coat and scarf wearing man looking for a companion deduces crime scenes - except the murderer is a creature from out of this world.
There's a sequel, Beastly Bones, as well, but I haven't read it yet.
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I like the sound of that. I went to add it to my "To Read" shelf on Goodreads and found that it was already on there! So I've requested it from the library