A new report to the District of Columbia government shows that the city will spend at least $25 million more in the current fiscal year than authorized by Congress.

The District has often spent more than it collected in revenues, which accounts for its cumulative deficit of $284 million. But this is apparently the first time in recent, history that any city administration has knowingly exceeded not only its income but its congressional spending limit.

Most of the overspending is for welfare and Medicaid programs administered by the city's Department of Human Services. The only way to keep those programs under the limits set by Congress for the year, Mayor Marion Barry said in a recent interview, would be to withhold welfare checks in August and September. But Barry said that "as long as I'm sitting in this chair, I'm not about to order welfare checks not sent out."

The overspending projection, the latest in a long series of gloomy fiscal reports that have obliged the mayor to raise taxes, cut payrolls and services and defend his policies against strong criticism, was made by Laurence Fitzmaurice, an analyst at American Management Systems Inc. of Arlington. f

That is the data-processing firm that designed the city's computerized accounting system. The report was submitted to Edward G. Winner, assistant city administrator for financial management, and forwarded by the Barry administration to City Council Chairman Arlington Dixon.

Spending more money than Congress appropriates is a violation of a federal statute known as the "anti-deficiency act" and is punishable by a prison term of up to two years. However, knowlegeable legal authorities said yesterday that no one has ever been successfully prosecuted under the act. s

In any case, Barry insisted that "we won't violate the act. There are some very specific procedures you follow" to cover anticipated overspending, "and we will follow them to the letter."

He was referring to a provision in the act permitting exception for "emergencies involving the safety of human life, the protection of property or the immediate welfare of individuals" in cases where programs -- such as welfare -- are partially financed by the federal government. When the official responsible for such as program anticipates the overspending, the law requires that he "immediately submit a detailed report of the facts of the case to Congress."

Aside from the legal issues, analysts of the city's financial problems saw other implications from the probable overspending. For one thing, they said, it is likely to harden anti-District sentiment in Congress.

For another, they said it probably means that Barry's budget for the 1981 fiscal year, which begins Oct. 1, is skewed by at least the amount of the overspending. The budget is theoretically balanced, but this year's anticipated expenditures were used as the basis for calculating next year's, and it is now apparent that those calculations were far too low.

The long-range financial plan that Barry issued on July 21 projected that the District would finish the current fiscal year with an operating deficit of $125 million -- that is, would spend $125 million more than it took in. That report did not address the issue of whether the spending contributing to that deficit would also exceed the city's appropriation from Congress.

It is clear from Fitzmaurice's report, however, that Barry was alerted to that possibility some time ago. Fitzmaurice refers to a report prepared by Winner on June 3 that projected that the city would overspend its congressionally authorized spending of $1,426 billion by $56.9 million.

Since then, Fitzmaurice noted, Congress has raised the appropriation by $42 million, but the rate of spending has also increased. Holding the total overspending for the year to $25 million, he said, presumes "that additional executive action is taken to ensure that identified potential savings are achieved."

In addition to continuation of the city's hiring freeze, he said, further savings would have to be made in the fire, transportation, police and environmental services departments and at D.C. General Hospital and the University of the District of Columbia.