New York City may be spurned for Dallas if the prestigious Museum of the American Indian accepts a tempting offer from a Texas billionaire.

"It would be one-of-a-kind in Dallas," said computer entrepreneur H. Ross Perot, whose $70 million bid could bring the city a billion-dollar collection of Indian artifacts that has languished for years in an inadequate Gotham building. "In New York, it would be just another museum."

But the city that never sleeps is not about to be caught napping on what could be an unprecedented ethnological steal. Since the museum first announced its intent to move in late February, New York officials have promised hefty appropriations if it stays and a court battle if it leaves.

This strategy appears to be working. At a meeting yesterday among city and museum officials, Mayor Edward Koch pledged full support, and museum chairman Barber Conable Jr. extended the ongoing discussions on pooling resources with the city's American Museum of Natural History.

"The decision today was a non-decision, to provide our trustees with more time," said Indian museum director Roland Force. "Our trustees have a lot of concerns still."

Only last Thursday, New York's chances looked bleak. The Indian museum's board of trustees voted 8-3 for Perot's bid and against the Museum of Natural History's: $30 million to build a new Indian complex within its Central Park West location and an annual $7.5 million for operations during the first 10 years, in addition to $13 million each from the city and state earmarked for the building project.

Although the Museum of Natural History pledged more money, Force considered Perot's offer more reliable. "It all depends whether you want a bird in the hand or two off in the bushes somewhere," he said, noting that the Natural History museum's bid hinges on fundraising and city and state allocations.

But Herb Kurz, manager of public affairs for the Museum of Natural History, asserted that the money is there. "We will raise $30 million for the complex ," he said, "and if we can't raise it, we'll take it out of our endowment" -- some $83 million.

Escape from New York will not be easy. The Indian museum's 1916 deed of trust requires that it serve the people of New York, and in order to leave the city it must first persuade the New York Supreme Court that it lacks the support necessary to operate there. State Attorney General Robert Abrams has promised a court fight if the museum tries to jump town.

The latest confrontation is only another chapter in what has been a 10-year-old story of dwindling attendance and crowded facilities for the Museum of the American Indian. Its location, on 155th Street and Broadway, is perceived by some as dangerous and by others as simply inconvenient. Last year the museum drew 35,000, compared to the 2.5 million who visited the Museum of Natural History.

Those who actually made it to the Indian museum saw only 4 percent of its collection. Due to limited space, most of the museum's 1 million artifacts are stored in a Bronx resource center that is closed to the public. At one point in the early 1970s it sold precious items to pay its staff.

The troubled museum has been negotiating with the Museum of Natural History for three years, and prior to approaching Perot it seriously considered offers from Las Vegas and Indianapolis.

If the museums linked, "it would be the greatest collection of native American culture in the world," said Richard Bruno, assistant commissioner of New York City's Department of Cultural Affairs.

But Force fears the Natural History museum would swallow the smaller museum. "They would want to ultimately take over the Museum of the American Indian and make it a part of their museum," he said.

Tom Nicholson, director of the Natural History museum, responded, "I don't think they've ever asked to remain autonomous."

The Museum of Natural History has proposed that the new Indian museum be governed by 18 Indian museum trustees and 18 Natural History museum trustees, who would be joined by six jointly appointed members and ex-officio members representing the city.

Force said this proposal would put Indian museum trustees in the minority. "We're not interested in being eaten for lunch," he said.

"I think that they have made up their mind about what they want to do and are using any explanation they can to justify it," Bruno said.

As the charges ricochet, each side positions itself more carefully for a possible court battle. Attorney General Abrams has subpoenaed all of the Indian museum's financial records and "memoranda, studies, reports, notes" relating to its plans for Dallas.

And lingering in the background is Perot, chairman of the Dallas-based Electronic Data Systems Corp., a subsidiary of General Motors. Last year Perot purchased a 700-year-old copy of the Magna Carta, which is currently on exhibit at the National Archives. This year he made the single largest individual offer the Museum of the American Indian received.

"It's the only world-class museum we could have in Texas," Perot said. "Museums don't move."

Asked whether he thinks the Indian museum might be using him as leverage against the Museum of Natural History, he said, "Yes. I'd have to be asleep not to think that."

Then he added, "I don't ever mind being used for a good cause."