A vice president of one of the nation's largest underwriters of tax-exempt municipal bonds believes investors will be wary when the District of Columbia government takes its first plunge into the private securities market later this year.

"Everyone grants that Washington is . . . unique because it is the nation's capital," Amos T. Beason of The First Boston Corp. said last week. "Because it hasn't sold securities before, most people don't know much about it."

Another top executive of a major New York capital markets group explained that investors are often puzzled by the city's relationship with Congress and the uncertainty, from year to year, about the size of the federal payment to the District.

"Whenever you're dealing with the District, the initial reaction among investors is that you're dealing with the whim of Congress," he said. "It makes you nervous."

In an attempt to end the District's historical reliance on the U.S. Treasury for loans when it needs money for long-term projects or to cover temporary cash shortages, the city soon will try to raise that type of money in the private bond market.

Its success will depend largely on the opinions of these and other Wall Street underwriters and analysts, who, guided in part by the credit ratings bestowed on Washington by Moody's Investors Services Inc. and Standard & Poor's Corp., will determine whether to acquire the District's notes and bonds for resale to their customers.

The analysts' and underwriters' dispassionate decision making also will provide the first real market test of Mayor Marion Barry's success in dealing with severe financial problems that have plagued his administration since he took office in 1979.

Until now, the District has obtained virtually all of its short-term and long-term financing from the Treasury. Last year, for instance, the city borrowed a total of $285 million. The city's total debt to the Treasury is $1.69 billion, according to the office of the deputy mayor for finance.

But the Treasury plans to cut off those loans next year, and that move is forcing the city into the private capital markets.

City officials see this as a mixed blessing. While there will be no more interest-free Treasury loans to cover temporary cash shortages, there also won't be any more higher-than-market interest rate Treasury loans for construction projects.

The city isn't a total stranger to the bond market. It was granted special legislation to issue a total of $55 million in revenue bonds, in 1981 and 1982, to finance construction at George Washington University. Last September, the D.C. Housing Finance Agency issued $52 million in revenue bonds to finance multi-family housing.

District officials say the city will "test the market" late this fall by seeking to issue about $140 million in short-term notes, which are repayable within a year. The city will wait until 1984 to attempt to issue general obligation bonds for capital improvements, officials said.

Gerald A. Fallon, a New York vice president of E.F. Hutton & Co., said last week the District probably would have little trouble in marketing short-term notes.

"Certainly there have been worse credits that have been able to raise money in the municipal market," Fallon said.

But long-term bonds, which often tie up investors' funds for 30 to 40 years, depend more on brokerage firms' confidence in the fiscal integrity of the municipalities issuing them. The brokerage firms bid for the right to market the bonds. The interest rate the District will have to pay investors for using their money will depend on how fiscally stable the underwriters' deem the District.

Some analysts interviewed last week appeared rather bullish on the District's prospects for marketing long-term bonds. They cited Barry's success in balancing the general operating budget the past two years and his issuance of audited D.C. financial statements for the first time in history.

"I think the Barry administration has made progress in the financial management area," said Karen Gifford, vice president of Merrill Lynch's Capital Markets Group in New York. "And that's all to the District's advantage when it comes into the financial market."

"There's a good bit of educating that needs to go on," Gifford added. "It's like a brand new company going public. . . . The critical thing is that they District officials have a credible plan for dealing with any budget deficits that might arise and an organized sales plan for the securities industry."

A former U.S. Treasury official, who now works for a Wall Street investment firm, agrees that the District "has come a long way" in improving its financial management techniques and shouldn't have too much trouble entering the municipal bond market.

"The mayor is on the right track," said the analyst, who asked that his name not be used. "But they city officials are going to have to do a lot of work to get up to speed on some things. Wall Street demands a lot."

The city must be prepared to explain how it intends to deal with a wide range of serious financial problems that face the city.

For instance, the city's employe pension program suffers from a massive unfunded liability; the water and sewer fund is running up huge deficits. The administration also hasn't developed a plan that is acceptable to Congress for dealing with a nagging $296.4 million accumulated deficit that could increase this year.

Franklin D. Raines, a private financial adviser retained by the city, said recently that the District's most pressing task in winning Wall Street's confidence is devising a plan to eliminate the accumulated deficit gradually as a way to demonstrate the city is serious about paying its bills.

"We've been going through a process of trying to educate the outside world about the District and to educate the District to how the outside world thinks," explained Raines, a member of the Lazard Freres & Co. investment firm. "What's not done is some conclusive action on the accumulated deficit."

Since taking office in 1979, Barry has unveiled several ill-fated plans--all hinged on assistance from Congress or federal agencies--for whittling down the deficit. The most recent plan has languished on Capitol Hill for two years and Congress has given Barry an April 15 deadline to come up with yet another plan.

But the mayor said recently he isn't certain that such a plan is necessary for the successful marketing of municipal bonds.

"There are some financial advisers who say we can go into the market as we are now," Barry said. "We'll see . . . . The final analysis, the final test of who is right or wrong, is to go into the marketplace and see."

Meanwhile, the city is gearing up for its entrance into the market. Deputy Mayor Ivanhoe Donaldson confirmed last week the administration is considering either replacing its current bond counsel, attorney James L. Hudson, or retaining additional firms to supplement Hudson's legal advice on the issuance of bonds.

Donaldson said that the law firm of Robert Washington Jr., a close political ally of the mayor's, may be retained as a bond counsel. Other firms reportedly under consideration include Sidley & Austin, Woodson & Woodson, and Reynolds Munday & Gibson.