Confess, Fletch — Gregory McDonald

Irwin Fletcher, a.k.a. Peter Fletcher or whatever name might prove convenient. Back from Europe with another promise of marriage, a mysterious death, and a fortune in lost paintings behind him.

What appears to be a simple apartment swap turns into a web of intrigue when Fletch finds the flat over-decorated with a beautiful corpse.

All the evidence points out that only one person could have committed the crime, and Fletch doesn't think he did it. The police think differently, though, and if Fletch won't confess, he'll need to find the murderer, himself.