BOOK REVIEW : Half-Baked Mystery of the Upper Crust : CARRIAGE TRADE, <i> by Stephen Birmingham</i> ; Bantam; $21.95, 480 pages

When it comes to the folkways of the rich, the powerful, and the privileged, Stephen Birmingham knows what he’s talking about. He has chronicled what passes for the American aristocracy in a couple of dozen books (“Our Crowd,” “California Rich,” “Life at the Dakota”). And his latest novel, “Carriage Trade,” is set in the same glitzy neighborhood.

“Carriage Trade” is the story of Tarkington’s, a fictional Fifth Avenue department store whose founder, Silas Tarkington, is found dead under suspicious circumstances in the swimming pool of his country estate.

Right from the start, we are allowed to understand that there is something rotten in the life and death of Si Tarkington, and Birmingham spends the next several hundred pages rooting out the dirty little secrets of the Tarkington family.

Indeed, “Carriage Trade” is a distinctly old-fashioned novel, a whodunit superimposed over the story of a family business dynasty, and it’s the mystery surrounding Si Tarkington’s death that gives Birmingham an excuse to luxuriate once again in the lifestyles of the rich and famous.

Tarkington’s, we are given to understand, is a unique institution where uniformed maids circulate with finger sandwiches, where no ladies garment is available in a size larger than 10, and where, at one point in the recent past, the woman in the next changing room might well have been the Duchess of Windsor.

“Her father’s magical store, dark now in honor of his memory but still full of his life,” muses Miranda Tarkington on the day after his death. “As always, the sight of the grand old building . . . evokes a little inner gasp of wonder.”

Birmingham actually kicks off “Carriage Trade” with a device so hackneyed that it has become the stuff of parody: the reading of the will. And, of course, he uses it as a neat device for introducing us to the cast of characters, each of whom is a potential suspect in Si Tarkington’s death: Consuelo, his calculating second wife; Blazer, his no-goodnik son; Miranda, his too-good-to-be-true daughter; Smitty, his latest mistress; Jake Kohlberg, his trusted lawyer, and so on.

Tarkington is dead and gone by the time the book opens, but we are given lots of dirt about him--his genius for selling overpriced schmates to rich women, his relentless philandering, his endearing little quirks (Chivas and Cheese Doodles), his dubious origins and his questionable business associates. Every once in a while, Birmingham has one of his characters remind us that Tarkington’s may be an institution of grace and elegance, but the fact remains that “retailing is--a jungle ,” as Connie Tarkington is given to say.

Birmingham brings a practiced hand to “Carriage Trade,” and he is perfectly capable of sharp, stylish prose, even if he sometimes indulges in a kind of wry self-parody. “This is not a fashionable address,” he writes of the law offices of Jake Kohlberg. “It is merely good.”

And yet, all too often, Birmingham appears to get lazy and slips into the formulaic writing of the trash novel, where brand names take the place of character description (“Tommy Bonham tosses his Mark Cross briefcase in a chair, kicks off his Gucci loafers . . .”) and everyone keeps reminding each other what lovely people they are, darling.

“Those shades aren’t going to help you one damn bit,” says Jake Kohlberg to Connie Tarkington as they cross the street. “You’re still one of the 10 best-dressed women in the world.”

At times, Birmingham indulges in some rhetorical high jinks, maybe just to keep himself from getting bored. He gives us unedited transcripts of interviews, long newspaper articles, and he even introduces one character--the memorable Moe Minskoff, a low-life schemer who slinks out of the shadows after Si’s death--in an extended scene that is rendered entirely in dialogue and stage directions. In fact, Birmingham insists on narrating the entire book, from beginning to end, in the present tense, so that the whole thing begins to sound like the first reading of a new play.

“Carriage Trade” chugs through the saga of the troubled Tarkington family with the efficiency of an on-schedule train, pausing only for the shocks and surprises that come up as predictably as the next station on the line. I was not surprised by the destination, but, then, I did not regret going along for the ride.