SO WHAT is new about a crime story set in Miami? Read Charles Willeford's New Hope for the Dead (St. Martin's, $14.95). It's both tough and funny with full-bodied characters, a murder solved with a new twist in detection, and a Miami scene as pulsating as the soundtrack of TV's Miami Vice.

And there is Sgt. Hoke Moseley, who emerges as a very human figure with strengths and faults that blend into a thoroughly likable character. Hoke, who made his debut in Miami Blues, is assigned to review "cold case" files by his boss, who is angling for a promotion. On the side, Hoke keeps digging into the death of a teen-age punk because of a nagging doubt that it may not be just another routine drug overdose. Moreover, the teen-ager has a sexy stepmother.

While juggling old files and the drug overdose, Hoke has to look for an affordable place to live since he must move to meet departmental regulations that cops live within the borders of the city. It's not easy since every other paycheck goes to his ex-wife to support two daughters whom he hasn't seen for years.

Then the girls, now 14 and 16, arrive on his doorstep. The ex-wife bought them bus tickets to Miami and has taken off for California to marry a baseball player who earns $325,000 a year as a pinch-hitter. So Hoke has to take the girls into the shabby hotel suite that he gets free in exchange for security services. Soon they are joined by Hoke's new partner, Officer Ellita Sanchez, banished from her home by a strict Cuban father irate over her pregnancy.

Hoke's relationship with his daughters is portrayed without sentimental claptrap. He never missed them during years of separation, but now that they are with him, he will take over the duties of a father. There is a marvelous scene in which he talks to them about sex in the language of the squad room.

Earlier, warning his daughters about the danger of the streets of South Beach, Hoke tells them: "If you had a doll, and you left it out overnight on the front porch of the hotel, it would probably be raped when you found it in the morning." The girls giggle but get the point.

New Hope for the Dead is a top-notch crime novel, both dark-humored and warmly human. Willeford deftly weaves the threads of several sub-plots while keeping up the suspense of how Hoke can prove murder (solved in bed) and find a house for his daughters and pregnant partner.

Bark and Bite

DICK LOCHTE's Sleeping Dog (Arbor House, $15.95) is a first mystery novel with audacious ingenuity and bouncy verve. Lochte, a Los Angeles book columnist, boldly essays split-narration, alternating between a middle-aged, thrice-divorced, weary private eye and a precocious 14-year-old with the brashness of a teen- ager who has seen and heard it all.

It begins when Serendipity (Sarah) Dahlquist tries to hire Leo Bloodworth to find her lost dog. Leo fobs her off on Roy Kaspar, who shares his office. When Kaspar is murdered, Bloodworth has a hard time explaining to Sarah that the slimy Kaspar was not to be avenged of her favorite movies: "When a man's partner is killed, he's supposed to do something about it."

A reluctant Bloodworth, who can't shake the persistent teen-ager who has become "the scourge" of his middle age, agrees to look after Sarah while her grandmother, a famous TV soap opera star, is in the hospital. Sarah's mother, Faith, a flower child of the '60s, shows more interest in her lovers than in her daughter.

The search for the dog escalates to mayhem and murder as Bloodworth and Sarah follow a trail that leads them to the Mexican Mafia, cruel dogfights, a banking scam, and a psychotic killer confronted in a chilling scene at a punk rock show.

Lochte deftly handles the split-narration with the alternating storytellers picking up the tale without overlapping. He does try to do too much in his first novel. Coincidences pile up at the end, and Sarah sometimes is just too smart. Still, Sleeping Dog is a charmer, and Bloodworth and Serendipity are a most appealing pair.

Castle Capers

A POSH health spa located in an old castle on the Yorkshire moors is the setting for a dandy mystery debut by a newcomer, Nancy Livingston, in The Trouble at Aquitaine (St. Martin's, $12.95). "Aquitaine Castle was built as a gift for his wife by Henry the Second. On their tenth wedding anniversary he imprisoned her in it . . . "

Dr. Hugh Godfrey, who has come to the clinic to lose weight and an ulcer, listens to the welcoming receptionist and wonders if he could imprison Marion, his unfaithful wife, "in their four-bedroomed detached or was there something forbidding it in the mortgage?"

He soon finds himself on a liquid diet and a rigorous schedule of exercises and massage. His fellow guests are an odd assortment, including an insufferable TV producer, his attractive woman companion who wonders why she ever started an affair with him 10 years ago (but then he was an up-and-coming young talent), a hearty woman who jogs, a woman with social pretentions, and tall, fit Valter Von Tenke, a mystery guest who seems to be an old friend of the owners of the spa, Col. and Mrs. Willoughby. For Von Tenke, the rest cure does not work. He is found dead, floating in the solarium pool.

Soon G.D.H. Pringle, who does not inspire confidence at first sight, arrives on the scene, hired as a private investigator by the owner's brother. A retired tax inspector with a calculator-precise mind, Pringle proves to be a shrewd investigator, unearthing secrets linking several of the guests to Von Tenke's past in the Far East.

Livingston has a lively wit that can be deliciously wicked at times. She reserves a warm, second-time around romance for Dr. Godfrey, a nice chap who blunders into embarrassing situations and can't help making a tentative diagnosis of goiter while being questioned by a policeman with bulging eyes.

Death at High Table

IN Academic Murder (St. Martin's, $15.95) murder almost does become academic. Dorsey Fiske's first novel is billed as "a mystery set in the halls of Cambridge," and we get much more of Cambridge than we do of mystery.

Fiske, who was a Yank at Cambridge as a research student, obviously came away with a deep affection for all things Cantabrigian. We learn about nearly all of them. First, though, there is a murder. Port is being passed along the high table of Sheepshanks College, Cambridge. Garmoyle, the sour librarian, already having imbibed more than a gentleman, signals for another decanter, takes a sip, and collapses in a crash of breaking glass. The port had been poisoned with arsenic.

It was Garmoyle who had discovered the holograph copy of what had been accepted by many scholars as one of Shakespeare's earliest poems. Ironically, Fiske wrote of her fictional discovery at Cambridge before the recent controversy over the love lyric attributed to the Bard found at rival Oxford's Bodleian Library.

The Cambridge background does have its moments with Fiske's sharp observation of academic rivalries and eccentricities. She is a literate writer but overgenerous with her erudition.

Beach Blanket Murder

DESPITE ITS mishmash of a plot, Jim Stinson's Double Exposure (Scribner's, $13.95) does offer some wryly amusing glimpses of the tawdry fringes of the Hollywood film industry.

Stoney Winston, who has a collection of rejection slips to match the feature scripts that he keeps writing, ekes out a precarious living directing cheap soda-pop TV commercials on the beach. Fortunately, his rent is cheap, and his landlady, a sexy computer programmer, provides both meals and comfort.

Stoney's sleazy producer-boss pulls him off his latest TV commercial shoot to retrieve a porno film starring the 18-year-old stepdaughter of a girlfriend. The mother is being blackmailed because the hard-core porn could cause her to lose her biggest client -- a TV evangelist who uses her run-down studio to film his money-raising pitches-cum-sermons.

If Stoney writes scripts like that of Double Exposure, it's no wonder why he gets rejection slips. There is nothing very original in another remake of the overused plot devices of porno flicks and greedy preachers. Stinson tries to pack too much into his first novel, and the result is a clutter of bodies and complications. Then, too, Stoney strains to be quirky, carrying on imaginary conversations about the case with the likes of Woody Allen and Sigmund Freud. Stinson writes with an easygoing, breezy style and deserves another chance with Stoney and a simpler story line.