A relatively small asset that could cause major problems was found among the many unexpected assets revealed in the bankruptcy of the cryptocurrency exchange FTX: a stake in one of the smallest banks in the nation.

Farmington State Bank in Washington State only has one branch and three employees as of this year. It didn’t even provide a credit card or online banking.

The relationship between the tiny bank and FTX’s demise has led to new inquiries about the exchange and its workings. Among them: How integrated into the larger financial system is FTX, which had its headquarters in the Bahamas? What else could the authorities have missed? How will Farmington become involved in the massive bankruptcy while searching for FTX’s missing assets?

Farmington State Bank and FTX started working together in March after Alameda Research, a tiny trading company and sister company of FTX, invested $11.5 million in FBH, the bank’s parent company.

Out of 4,800 banks in the country at the time, Farmington was the 26th-smallest bank. According to the Federal Deposit Insurance Corporation, it had a net worth of $5.7 million.

Ramnik Arora, a top aide to the exchange’s creator Sam Bankman-Fried, oversaw the investment by FTX, which financial regulators claim was more than double the bank’s net worth. Many of the much bigger deals that FTX made with Sequoia Capital and other venture capitalists that ultimately fell through were the result of Mr. Arora’s work.

Farmington is connected to various crypto networks. Bank was purchased by FBH in 2020. Jean Chalopin, the chairman of Deltec Bank, which, like FTX, is based in the Bahamas, and a co-creator of the 1980s cartoon cop Inspector Gadget, is also the chairman of FBH. The most well-known customer of Deltec is Tether, a cryptocurrency company with $65 billion in assets that provides a stablecoin pegged to the dollar.

Because of its reclusive owners and offshore bank accounts, Tether has long faced financial concerns. FTX was one of Tether’s biggest trading partners through Alameda, which led to worries that the stablecoin might be connected to FTX’s fraudulent activities without anyone being aware of it.

Farmington’s deposits had been consistent at around $10 million prior to the acquisition. 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.

What F.T.X. had in mind for Farmington is unclear. Farmington is now known as Moonstone Bank online. Just a few days before F.T.X.’s investment, the name was trademarked. There is nothing about Bitcoin or other digital currencies on the Moonstone website. According to the statement, Moonstone wants to aid “the development of next generation finance.”

It’s unclear how FTX obtained a bank license in the United States, which would require approval from federal regulators. Veterans of the banking industry find it difficult to believe that regulators would have knowingly allowed FTX to take over 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.”