Find the Lady, by Norman Firth (epub/Kindle)

Mike Spagliotti, the big-time racketeer, had enjoyed a successful life of crime, managing to evade police arrest. But that life had met a sudden and violent end, when he was found shot through the head in his New York hotel suite. He had seemingly died alone—with the doors of his suite locked. Two of his thugs were standing guard over him in the passage, as usual—and they swore they had heard nothing. The gun must have had a silencer. But the guards also swore they had let no one past.

A perplexing problem for the Detective-Inspector Flannel, of Homicide, whose fiery temper is not improved when a troublesome lady newspaper reporter involves herself in his investigation!