FICTION : GREENWICH KILLING TIME by Kinky Friedman (Beech Tree /Morrow: $13.95; 196 pp.)

This is a very kinky mystery--but don’t get the wrong idea. The story does have some sexy bits, but nothing shocking. It’s just that the wisecracking, cigar-smoking sleuth is named Kinky, whose twangy urban banter brings to mind the onstage persona of the author, Kinky Friedman, better known as a country singer and songwriter, here making his fiction debut.

The violence is steady and the motives are suitably twisted for a murder tale set in New York’s Greenwich Village, perhaps the least appealing neighborhood in the world on weekends. A bisexually active young man is found with a hole in his head, and the cops are trying to pin the crime on Kinky’s buddy McGovern, a Daily News reporter. Out to clear his friend, Kinky tracks down the dead man’s numerous jilted lovers, both male and female (this is the Village, after all). This all leads through the usual back alleys, hounded by typically unimaginative cops, chasing women too beautiful to be good and cornering some outrageous genre cliches--for example, he actually enters a murder scene thinking: “It was quiet. Too quiet.”

Shamus on you, Kinky.

At times, sorting through the various players is no easy job. Indeed, if our narrator didn’t occasionally stop everything to summarize the plot for us, we’d be lost completely. Though he’s no Raymond Chandler, Friedman does endow the story with a certain gritty charm, and his hero oozes a brand of self-reductive irony, by now quite familiar to readers of American detective fiction.

If you can weather its storm of bad similes and jokes, “Greenwich Killing Time” has a swell ending involving some lines of cocaine and a classic one-liner: “You killed two birds and got stoned.”