By Tony Hillerman

Harper & Row. 292 pp. $19.95

IT'S OFFICIAL. Summer can begin now. Tony Hillerman has written another in his Lt. Joe Leaphorn-Officer Jim Chee series about mythology, murder and mystery on the Navajo reservation in the Southwest.

Coyote Waits begins innocently enough, with Delbert Nez, one of Chee's colleagues on the Navajo Tribal Police force radioing Chee that he's pursuing a vandal who for unknown reasons has been painting rocks; after he catches the culprit, Nez tells Chee over the radio, he'll meet Chee for a cup of coffee at a roadside diner. Rather than follow police procedure and provide backup as he knows deep down he should, Chee proceeds to the diner. When Nez fails to show, Chee goes looking for him and, of course, finds him dead in his burning police cruiser.

Within minutes Chee has arrested a suspect, an old, drunk Navajo wandering along the road in the rain. But the man refuses to say anything except "I am ashamed."

Hillerman presents himself with an interesting problem. If he strings us along for the entire story and then winds up with the murderer being the old man, Ashie Pinto, he leaves his readers disappointed. The conventional approach would be to leave Pinto in jail until the end and then establish his innocence by having Chee -- or Leaphorn -- pin the murder on someone else. This isn't a conventional story, but the solution isn't disappointing, either.

Coyote Waits isn't so much a whodunit as it is a whydunit and the story presents two separate mysteries. Who killed Nez? And who is the vandal and what is he (or she) doing? Chee solves one mystery and Leaphorn the other. By having both men working on the case -- independent and suspicious of each other -- Hillerman is able to increase the tension while plausibly keeping the two protagonists in the dark. A subsequent murder only deepens and complicates the mystery.

But, as with all of Hillerman's mysteries, Coyote Waits isn't simply a crime story. It is also rich in Navajo folklore and philosophy, providing a window on another culture, a view of a proud and intelligent people living in our midst, struggling with demons of their own and those that the white man sets upon them.

The "coyote" of the title is mischievous, malignant fate, omnipresent and always ready to work evil when given a chance. When a Vietnamese woman describes a saying in her country that "fate is as gentle with men as the mongoose is mice," Chee responds that the Navajos "say the same thing in different words. We say: 'Coyote is always out there waiting, and Coyote is always hungry.' "

Using Leaphorn and Chee to solve the murder does allow an intriguing blend of basic common sense and romanticism, pure police work and anthropological and mythological inquiry. Leaphorn, knowledgeable about but hostile to his Navajo mythology and tradition, is solid and steady, wanting to know why the vandal was painting an outcropping of rocks. Chee, who prides himself on his heritage, chooses to investigate Pinto's possible motives, looking for clues -- successfully ultimately -- in the suspect's recorded telling of Navajo legends.

The somber mood of the book is enhanced by the subtext on the destruction and mayhem that alcohol causes among Native Americans. Hillerman touches on this theme in other books in the series and he handles the subject without heavy-handed moralizing.

Coyote Waits isn't, however, without its problems. Because Hillerman is interested in the psychology of his protagonists, he apparently thinks it's unnecessary to give us much of an idea of what his characters look like. Leaphorn and Chee are described in only the vaguest ways and he doesn't do much better with the supporting cast. That is not to say that this is a story populated with stick figures. The personalities come across quite well. In Navajo terms, Hillerman devotes a great deal of attention -- as he should -- to the inner form of things, but stints on the outer form.

Leaphorn, for Hillerman devotees, appears to be getting over the death of his beloved wife, Emma. He appears to be developing a romantic interest in a professor of American studies. And Chee resumes a friendship -- it never is more than that in the book -- with Janet Pete, a Navajo defense lawyer. This is all perfectly tame and chaste without even any heavy breathing, which is fine. The story doesn't need sex to make it better than it already is.

The story has two other problems that don't detract from its enjoyment but are nonetheless bothersome when reading someone who obviously takes as much care in his plotting as Hillerman does. Chee inadvertently causes, or at least sets in motion, the second murder in the book when he reveals a seemingly insignificant piece of information to one of the characters. But Chee, who is so racked by guilt over his failure to provide backup for Nez, doesn't acknowledge that his unauthorized meddling in the murder investigation results in a second killing.

And, Hillerman, by the way he chooses to wrap everything up, would like us to overlook that if Chee and Leaphorn had done nothing, most of the important questions surrounding Nez's death would have been answered in due course without any police investigation.

But then, we wouldn't have had the pleasure of being absorbed in this otherwise first-class mystery. Coyote Waits probably isn't Tony Hillerman's best, but it's more than good enough, a well-paced, deftly plotted, nicely written addition to his work.

Lawrence Meyer, editor of The Washington Post National Weekly Edition, is the author of the mysteries "False Front" and "A Capitol Crime."