Among the many surprising assets uncovered in the bankruptcy of the cryptocurrency exchange FTX is a relatively tiny one that could raise big concerns: a stake in one of the country’s smallest banks.

The bank, Farmington State Bank in Washington State, has a single branch and, until this year, just three employees. It did not offer online banking or even a credit card.

The tiny bank’s connection to the collapse of FTX is raising new questions about the exchange and its operations.Among them: How closely tied is FTX, which was based in the Bahamas, to the broader financial system? What else might regulators have missed? And in the hunt for FTX’s missing assets, how will Farmington get dragged into the multibillion-dollar bankruptcy?

The ties between FTX and Farmington State Bank began in March when Alameda Research, a small trading firm and sister to FTX, invested $11.5 million in the bank’s parent company, FBH.

At the time, Farmington was the nation’s 26th-smallest bank out of 4,800. Its net worth was $5.7 million, according to the Federal Deposit Insurance Corporation.

FTX’s investment, which according to financial regulators was more than double the bank’s net worth, was led by Ramnik Arora, a top lieutenant of the exchange’s founder, Sam Bankman-Fried. Mr. Arora was responsible for many of the much larger deals that FTX signed with Sequoia Capital and other venture capitalists that eventually failed.

Farmington has more than one crypto connection. FBH bought the bank in 2020. The chairman of FBH is Jean Chalopin, who, along with being a co-creator of cartoon cop Inspector Gadget in the 1980s, is the chairman of Deltec Bank, which, like FTX, is based in the Bahamas. Deltec’s best-known client is Tether, a crypto company with $65 billion in assets offering a stablecoin that is pegged to the dollar.

Tether has long faced concerns about its finances, in part because of its reclusive owners and offshore bank accounts. Through Alameda, FTX was one of Tether’s largest trading partners, raising concerns that the stablecoin could have yet-undiscovered ties to FTX’s fraudulent operations.

Before the acquisition, Farmington’s deposits had been steady at about $10 million for a decade. But in the third quarter this year, the bank’s deposits jumped nearly 600 percent to $84 million. Nearly all of that increase, $71 million, came from just four new accounts, according to F.D.I.C. data.

It’s not clear what FTX’s plan was for Farmington. Online, Farmington now goes by Moonstone Bank. The name was trademarked a few days before FTX’s investment. Moonstone’s website doesn’t say anything about Bitcoin or other digital currencies. It says Moonstone wants to support “the evolution of next generation finance.”

Deltec and Moonstone did not return a request for comment.

It’s unclear how FTX was allowed to buy a stake in a U.S.-licensed bank, which would need to be approved by federal regulators. Banking veterans say it’s hard to believe that regulators would have knowingly allowed FTX to gain control of a U.S. bank.

“The fact that an offshore hedge fund that was basically a crypto firm was buying a stake in a tiny bank for multiples of its stated book value should have raised massive red flags for the F.D.I.C., state regulators and the Federal Reserve,” said Camden Fine, a bank industry consultant who used to head the Independent Community Bankers of America. “It’s just astonishing that all of this got approved.”