The Killer Touch — Ellery Queen

An American cop stumbles across a drug ring on a tropical island

No matter how hard she tries, Tracy can't seem to kill herself. Her hands shake too much to cut her wrists. Wading into the ocean, her body refuses to be drowned. Even the heroin she has been shooting for years has failed to kill her. Her joints aching, she takes another hit, promising herself that she'll attempt suicide again tomorrow. But she won't get the chance. Tracy's just sinking into her high when a man comes through the door, wraps his hands around her neck, and starts to squeeze.
 
Burt March lands on Isle de Trois soon after Tracy's murder. An American cop visiting the Caribbean to get over a recent near-death experience, he won't find the relaxation he's looking for. Isle de Trois may be beautiful, but it's dangerous. And March will discover that drugs, money, and murder are all it takes to turn paradise into hell.