Paris February 2016 497On Friday, a bright red 1957 Ferrari rolled onto a stage in Paris and sold for 32 million euros, or about $35.8 million, making it, by some measures, the most expensive car ever sold at auction.

The celebrated racing car captured the attention of wealthy car collectors around the world — as well as the interest of the French tax authorities.

The Ferrari was sold by the Bardinons, a prominent French family whose members are feuding with one another and the French government over their famous Ferrari collection.

For tax purposes, some members of the family initially valued its stable of over a dozen Ferraris at around 70 million euros, or $78 million. And yet experts say the collection could be worth over $200 million. Especially after Friday’s sale, the French tax authorities are likely to take a closer look at the family’s math.

“This case is like a thriller,” said Vincent Grandil, a leading French tax lawyer with the firm Altexis.

The battle over the Bardinon Ferraris highlights an increasingly popular tax strategy being used by wealthy families around the world. Art, vintage cars and other collectibles passed down to family heirs are often subject to estate taxes or gift taxes. Yet the values of these trophy assets can often be subjective. So some families are using special appraisers and selective data to value their family heirlooms and lower their tax bill.

The problem has become even more acute in recent years as the prices for fine art, cars and wine have soared, giving families more leeway in valuations.

“A valuation for a painting 10 months ago may not be valid today given what’s happened in the art world and the auctions,” said David A. Handler, a trust and estates lawyer with Kirkland & Ellis who often advises wealthy families on valuing assets.

Mr. Handler said some clients asked him if they could simply avoid disclosing their costly paintings or collectibles to the Internal Revenue Service. “No one wants to pay more than they have to,” he said. “But I tell them, “If you try to hide it, there’s a good chance the I.R.S. will find out.’”

The I.R.S. rules surrounding fair-market value for collectibles are highly technical. The agency has a special panel of experts, called the Art Advisory Panel, that helps it determine values for big-ticket artworks claimed by taxpayers. The panel found that taxpayers were increasingly lowballing their art values.

In 2014, the panel looked at 54 taxpayers with 315 items valued at a total of $251 million. It challenged two-thirds of the valuations. The owners had valued the items at $103 million, but their actual total value was over $180 million, according to the panel’s annual report.

Conversely, rich taxpayers are overvaluing items they give to charity, increasing their deductions. The Art Advisory Panel report said the items it examined, valued at $3.8 million for charitable deductions in 2014, should have been valued at $1.7 million.

Patti Spencer, a trust and estates lawyer in Pennsylvania, said one of her clients gave a collection of dinner plates to a university and valued them at $200,000 for the tax deduction. The I.R.S. challenged the appraisal, and determined the value to be closer to $50,000, said Ms. Spencer, who advises her clients to be thorough and hire top appraisers.

“People just figure the checking on this stuff is so spotty, why not try?” she said.

The I.R.S. said its employees “have access to a variety of resources that allow them to stay abreast of changes in the art and collectible markets.”

On Friday, the Bardinon Ferraris brought the issue to the world stage. Pierre Bardinon, born in 1931, was an heir to the Chapal family, a French leather and fur dynasty famed for making pilot bomber jackets. As a boy, Bardinon fell in love with cars and started buying old racing Ferraris in the 1960s, when few other collectors were interested in them.

He went on to buy more than 70 rare Ferraris. He turned the family chateau at Mas du Clos, near Aubusson, into a Ferrari playground, with a museum housing the cars, and a two-mile racetrack.

After Mr. Bardinon died in 2012, and his wife a year later, the French government levied an inheritance tax of millions of dollars on their three children, according to court documents. The Bardinon siblings are now battling in court over the future of the collection.

The Ferrari collection had dwindled to around 20 cars by 2012, as Mr. Bardinon sold them off. Yet their value has soared. Classic Ferraris have led the recent explosion in collectible car prices; a Ferrari 250 GTO sold for $38 million in 2014 to become the most expensive car ever auctioned.

Marcel Massini, a Geneva-based Ferrari historian who knew Mr. Bardinon and frequently inspected the collection, said the remaining cars in the Bardinon collection could be worth over $200 million. He said at least three of them could fetch over $30 million each in today’s market.

“These are like the Mona Lisas of the Ferrari world,” he said. “They are the best of the best.”

And yet for tax purposes, certain members of the family valued the entire collection at 70 million euros, according to court documents.

As the court fight continued, two of the siblings decided to auction off a trophy of the collection, a 1957 Ferrari 335 Sport Scaglietti, the one that sold at an Artcurial Motorcars auction on Friday. Measured in euro terms, it was the most expensive car ever sold at auction, but measured in dollar terms, it ranked second. Lawyers familiar with the case say the sale could lead the French government to increase the valuation for the family’s collection — and demand more taxes.

The Bardinon family and their lawyers declined repeated requests for comment.

Some wealthy collectors hope that the situation could lead to more Ferraris being up for sale. “There are a lot of billionaires in the world who want these cars,” Mr. Massini said. “So I think they are very happy with the result. But I don’t know how happy the family is.”