The lady in the First American Bank branch was livid. If a bunch of Arabs are buying the bank, they aren't going to get my money, she warned the manager in front of a lobby full of customers.

Assured the Financial General banks have not yet been sold -- and perhaps may never be -- the irate customer was talked into keeping her account open, but the manager never addressed himself to the questions the woman and a lot of other people are asking:

What is going to happen to Financial General Bankshares now that an agreement has been signed to sell the $2.2 billion bank holding company to three Middle Eastern investors?

Will the First American Banks become the first Arab banks in the nation's capital?

Will the new owners pour in petrodollars and build Financial General into an internationally financed rival to Riggs National Bank and American Security Bank for leadership of the Washington financial community?

Will the traditional local autonomy of the Financial General banks be replaced by management from Mecca or absentee arrogance?

Inside Financial General -- and in the offices of its individual banks -- there are plenty of people who share that outraged customer's concern. "Offhand I can't think of anybody at Financial General who wants to see the banks sold," says one Washingtonian with a lot of contacts in the organization. Off-the-record interviews support his contention.

Some people at FG also say privately they think the banks will never be sold, despite the agreement signed by Chairman F.B. Saul II.

Five states, the Comptroller of theCurrency and the Federal Reserve Board have to approve the deal. That regulatory minefield could blow up the agreement, the naysayers suggest. In addition there are growing demands in Congress for a moratorium on all purchases of U.S. banks by foreign interests.

Pessimism about the sale going through is evident also in the price of Financial General shares, which now are trading on the American Stock Exchange for about $24. The agreement calls for the Middle Eastern group to make a public offer of at least $28.50 a share and to raise their bid if, as expected, the book value of FG shares goes up before the offer is made.

If the sale is a certainty, there's $5 a share to be made by buying the stock today, but the speculators and arbitragers don't seem to be taking that bet. (On the other hand, the difference in price could reflect the interest cost of holding the FG stock for a year or more until the offer is made.)

It will take that long to get the necessary regulatory action to process the applications to buy the bank that are being prepared now by Robert Altman, the lawyer representing Kamal Adham of Saudi Arabia, Abdullah Darwaish of Abu Dhabi and Faisal Saud al Fulaij of Kuwait, the Middle Eastern investors.

The Federal Reserve Board -- which in principal does not object to foreign bank takeovers -- will make the final decision on the application, but banking regulators in the five states in which FG has banks will have a voice in the process.

State regulators in Virginia and Tennessee have already told the Fed they oppose the FG sale, and New York state banking director Muriel Siebert is on record against any more foreign takeovers of New York banks. Objections by the states will require the Federal Reserve to hold public hearings on the sale, prolonging the decision process.

The critical issues for the Fed will be the same ones troubling FG customers: What will happen to the banks, and who are these people?

Altman's clients will have to spell out in detail their plans for the banks.

The sale agreement says the Middle Eastern group, "will make only such changes [in the banks' management] as are necessary or desirable to improve their operations and competitive positions." The autonomy of the individual banks will be preserved, Sheik Adham has assured Financial General, but the board members of the banks are not convinced.

They also have talked generally about increasing the international business of the banks. None of the FG banks is now a serious factor in Washington's international banking, which is dominated by American Security and Riggs.

The Adham group's international banking connections, however, could prove to be more of a minus than a plus in getting Federal Reserve approval. In the two-year legal battle that preceded the recent sale agreement, FG lawyers spent a lot of time probing the links between Adham, Darwaish and al Fulaij and a controversial London financial institution called Bank of Credit and Commerce International.

The formal offer to buy Financial General will be made by a Netherlands Antilles company called Credit and Commerce American Holdings and Credit and Commerce Amercian Investment, a Dutch corporation.

BCCI has had several run-ins with British banking regulators. Controlled through a secret holding company, BCCI is believed to be owned by the ruling families of several Middle Eastern nations. Its founder, a Pakistani financier named Agha a Hassen Abedi, has been linked to questionable payments involving Middle Eastern business deals.

If there's any fire behind that smoke, it's likely to be stirred up by the Federal Reserve's examination of the Financial General deal. The Fed also will have to get details of the personal business connections of Adham, al Fulaij and Darwaish.

Anybody with the money can take over most U.S. corporations, but federal regulators are very careful about who buys banks. Obtaining and verifying information about the financial strength and stability of foreign investors is the one issue that most troubles federal banking regulators, and it could be the stumbling block of the Financial General takeover.