You may need a bloodhound to find one of the most offbeat museums in New York: the Dog Museum of America. It is kenneled deep within the baroque portals of the New York Life Insurance Building at 51 Madison Avenue. Only the guards within the building's marble halls know it's there. To stop a passerby and ask ''Do you know where the dog museum is?'' is to risk being growled at by New Yorkers who think their city is going to the dogs anyway and this museum they never heard of is just one more example.
But there it has sat at the corner of Madison Avenue and 25th Street for the last year and a half, a veritable monument to the chihuahuas, basset hounds, bichon frises, and Great Danes of dogdom.
When you bring up the idea of a dog museum in casual conversation, people's hackles sometimes rise.
''Is it full of stuffed dogs?'' they often ask with a shudder.
Let's clear that up right away. No. No stuffed dogs. There is not a single cuddly Steiff bowwow in sight for children.
The Dog Museum of America is a serious museum, established by the American Kennel Club (AKC) Foundation, according to its brochure, ''in recognition of its need to educate the public about the history and achievements of man's best friend.'' It is located in the same building where the AKC has its headquarters and a 700-volume dog library.
In fact, the museum is almost austere looking: battleship-gray walls hung with the current exhibit - generally paintings, black and white photos, or sculpture - and not a rubber bone in sight. The museum is now readying its fall exhibit, ''Hound and Horn,'' which will run from Sept. 13 through Dec. 2.
It illustrates the sport of fox hunting with 50 American and English works of art, including works by Richard Barrett Davis, whom English royalty from George II through Queen Victoria favored for his paintings of hunters and hounds; John Nost Sartorius of the sporting painter Sartorius family; Benjamin Marshall, a painter of hunting personalities and dogs; and Sir Alfred Munnings, who painted impressionistic hunting scenes. The exhibit on fox hunting (once defined by George Bernard Shaw as ''the unspeakable in pursuit of the uneatable'') will also include American hunt costumes, artifacts, and decorative objects.
The museum unleashes four shows a year; previous exhibits have included ''Best of Friends: The Dog in Art''; ''Color Me Dog,'' a holiday show for children; ''Fidos and Heroes in Bronze''; and ''The Dog World,'' subtitled ''The Measure of Man in His Kindness to Lesser Creatures.''
During a recent tour of the museum, there were several works of art from the permanent collection on display, a somber oil portrait of a mastiff by Arthur Wardle, Edwin Megargie's untitled portrait of a Great Pyrenees, and Samuel John Carter's ''Distinguished Foreigners,'' an oil of two poodles and a whippet. The museum has also acquired two paintings by Jean-Baptiste Oudry, the 18th-century court painter who ranks as a da Vinci of the dog world. An unsigned wood block of Queen Victoria appears with her faithful Yorkshire terrier at her side. A gouache by Ward Binks of German shepherds flanking a statue outside Geraldine Rockefeller Dodge's home is a clue to the founding of the museum.
When Mrs. Dodge passed on, director William Secord says, the dispersal of her unique collection of dog art and memorabilia led to the founding of the Dog Museum.
From behind a half-open grey door at the museum came a sharp little bark belonging to the Dog Museum's terrier-in-residence, a toy Manchester named Tommy. Tommy, a black and tan terrier who looks a bit like a mini-Doberman pinscher, guards the office of his master, Mr. Secord. His master, a young man with brown hair wearing a mocha-colored suit, appeared shortly after the bark. He pointed out that the museum has no founding endowment and is trying to raise presidential dogs, dogs in the White House, dogs in fashion.
Movie dogs have already been dealt with at least in part in the ''Color Me Dog'' exhibit, which included clips from ''Lassie Come Home'' and the ''Wizard of Oz'' dog, Toto. Children were invited to bring a photo of dogs to use as entrance tickets. But perhaps a whole show could be devoted to dog stars, with clips and stills from movies like the early ''Rin Tin Tin'' or ''Benji.''
Here are one visitor's suggestions for additional exhibits:
* For children, who are a natural audience for such a museum, there might be greater emphasis on bright colors, graphics, color photos, and a ''please touch'' exhibit of such dogiana as unique collars, leashes, muzzles, doghouses, and even nonvaluable art.
* Children who enjoy finding out what the different breeds of dogs are and where they come from might appreciate a dog map of the word. Or perhaps a colorful photo display of unusual breeds and even a dogs-at-work montage: sheep dogs herding, malamutes pulling sleds in the snow, Saint Bernards rescuing travelers, or even beagles ''beagling.''
* Dale McConathy's monograph for ''The Dog in Art'' exhibit, which is stuffed with fascinating dog history, might have special interest for children in a display just for them: for instance, a mock-up of the million-dollar royal kennels at Versailles, which Louis XIV constructed in 1685, with packs of Great Pyrenees used to hunt wolves, Scottish dogs for roe deer, other special breeds for hare and boar hunting. Or Louis XIII's hunt operation, which included four dog servants, 18 bloodhound guides, four knights of the kennel, 40 noble huntsmen, and two hunting pages.
* Finally, the Dog Museum of America might consider some identifying landmark outside the building it's housed in to give a hint that it's there. A retail clothing store on Fifth Avenue used to have a fountain outside its entrance for thirsty dogs, and that might be a discreet way to announce its presence - with a sign at Lhasa-apso eye level.