Is this a crime novel?
The crime novel genre is very wide and includes many sub-genres which in turn have sub-genres. There is the American mystery, the English mystery, the thriller and the police procedural, but within these categories there are historical mysteries, whodunits, pastoral cozies, spy thrillers, revenge thrillers, courtroom thrillers, paranoia or conspiracy novels, and many more.
Art Bourgeau, in The Mystery Lover's Companion, even divided police procedurals into subcategories: misdemeanors, felonies, manhunts, and trial-by-jury novels, citing examples of each sub-genre.
Then there are the cross-genre novels, such as mystery/westerns, suspense/romances, and political/thrillers. All of these categories can be written heavily or humorously, seriously or in parody, in superficial prose or literary depth. My favorites of these are multi-layered, with enough recalcitrance that different people will see them differently, often just a simple story revealing universal truths with clarity and compassion. In the form of a crime novel.
Think of Flann O'Brien's The Third Policeman and Graham Greene's The Third Man, with their trinities stacked to infinity. Are these crime novels too? Surely they are.
Death Is A Lonely Business was Ray Bradbury's tribute to the great detective yarns, written back in 1949 but revised and first published in 1985. It is dedicated to several people including "the memories of Raymond Chandler, Dashiel Hammett, James M. Cain, and Ross MacDonald."
The protagonist is the author himself, an everyman, but a guy noir, puzzling over life's persistant questions, seeking justice while trying to find solid logical ground on which to stand. He is followed around by his shapeshifting shade. When asked on page four to identify his shadow, the protagonist says only that he's one of the furies.
Set in historical Venice, California, where Bradbury lived for several years, the crime involves a disappearing circus and amusement park. The dead man may be a personified cat trapped in one of the submerged lion cage cars, which is pictured on the cover of a later edition of the novel. It's not quite the Dali death cart pictured on the 1985 first edition of Blood Meridian, but it will do--the phantom car conjuring up the cat in the cage.
The detective who helps to solve "the case" is named Elmo Crumley, an apparent allusion to James Crumley, noted author of The Last Good Kiss (1978) and other good ones.
Death Is A Lonely Business is a crime novel that is also autobiographical and humorous and literary, enmeshed in that rarefied atmosphere of noir, filled with nuanced surprises and grotesques, and ringing with universal truths about life and death.
Some of the jokes may have aged a bit. For instance, "Her round face was a moon watching over the vast territorial imperatives of her body." That isn't quite as funny now as it was when Robert Ardrey's The Territorial Imperative was on the bestseller lists. But the universals in here are timeless.
Death's friend is always selling tickets at the local theater, and the picture never seems to change. The only word on the marquee is always "Goodbye."