The muddled financial management of the District of Columbia's government is about to get a dose of the same corrective medicine applied to help reverse New York City's staggering economic debacle.

In both cases, a Nothern Virginia company started in 1970 by some of Robert McNamara's former Pentagon "whiz kids," American Management Systems, Inc., is prescribing the method by which a complex government superstructure can begin to keep track of its money and workers.

For District residents, who regularly become exasperated when trying to figure out their ocassional water and sewer bills, there was little surprise a year ago when the accounting firm of Arthur Anderson & CO. concluded that D.C.'s finance were a mess.

"The District and many of its separate agencies appear to have placed little, if any emphasis on providing accurate and reliable financial data to the public," said the accounting firm, which even recommended against any attempt to balance D.C.'s books because the result could be useless.

Instead, the path recommended for the city government was one of working primarily to develop a proper system for use in future years.

As a first step in that direction, Sen. Thomas F. Eagleton (D-Mo.), the man who blew the whistle on D.C. budget problems and who is chairman of a Temporary Commission on Financial Oversight, has announced the award of a $55,000 contract to American Managements.

"We conducted a competitive procurement in which many firms throughout the nation evidenceed interest," said Eagleton, expalining the choice of an Arlington firm for the job.

But it was American Management't unique role in New York City's financial crisis that enhanced the company's reputation as a management consulting and systems development firm - one capable of overhaulin methods by which the Districs's $1.5 bullion of annual expenditures are controlled.

New York's entire financial system was restructed in less than two years and American Management was the company that designed the plan, created computer programs for handling the data and providing leadership throughout.

In place of accounting practices largely unchanged since the 1920s. American Management used techniques previously developed in reorganizing the financial sturcture of such industrial giants as the Burlington Northern Railroad and K mart Corp. (formerly S. S. Kresge Co.).

With a $1.1 million contract from New York, American Management created an Integrated Financial Management System (1FMS), under which the city's new mayor will be able to relate budgets to expenses on virtually an instantaneous basis.

Ivan Selin, chairman of the Arlington firm and former chief of systems analysis at the Pentagon, said his company expects an annual volume this year of $18 million from solving problems of business and government, up from $12 million last year.

Selin has a goal of increasing business by 25 per cent a year for the next five years. His firm has grown from 5 to 140 professionals and now has branches in Boston, New York, San Francisco and Chicago. Some 60 per cent of revenues come from professional services and the balance from product-related activities.

The District government is smaller than that of New York but he scope of its management problems may be larger. Selin said. Initially, his firm will work two months to complete recommendations for D.C. money management. After that, specific plans well be selected and contractors will be hired to do the work - with American Management a leading contender.

MAGNIN COMING - They're not talking about it publicly yet, but executives at I. Magnin in San Francisco have March 29 marked on their calendars for the opening of Magnin's Washington area store.

It'll be on the second level at White Flint, midway between Lord & Taylor and Bloomingdales, which is Magnin's cousin in the Federated Department Stores family. The official announcement is being held up while federal regulagtors analyze some aspects of Federated's expansion program.

NEW SUPPLEMENT - Warren Adler, advertising executive, novelist and society publisher, has another venture brewing - a new Sunday newspaper supplement to rival Parade and Family Weekly.

Adler says any discussion of the project would be "premature." Nor is there any response from Smith Bagley, the Carter fund raise and tobacco heir who is said to be the financial man behind Adler's idea.

A mass circulation Sunday supplement would be at the opposite end of the publishing spectrum from Adler's other property, the magazine Dossier, which writes about and for society types.