The Reagan administration, beginning a long-anticipated crackdown on the District government's authority to dip into the U.S. Treasury, has asked Congress to terminate the city's right to take interest-free short-term loans whenever it runs short of cash.

That borrowing authority has been an indispensable financial tool for the District for decades. The city has borrowed as much as $80 million annually from the Treasury in past years and has already drawn $40 million in interest-free loans this year.

If that authority were eliminated, the District would have to borrow from banks or sell its own interest-bearing short-term notes on the commercial money market.

City officials are concerned that lenders might be unwiling to purchase securities issued by a government saddled with a $388 million cumulative deficit and a chronically unbalanced budget.

The adminstration also asked Congress to limit the amount of long-term capital borrowing that the city can do at the Treasury each year and to require that the District government pay an interest surcharge on whatever loans it takes.

If implemented, the measures could increase the city's borrowing costs, and, at worst, leave the city without resources for payroll and welfare payments during the cash-short months between tax collection periods, when short-term Treasury loans have been critical.

In effect, the budget-conscious Reagan administration is taking the home-rule city government at its word and trying to cut the District loose from the Treasury's purse strings.

The problem facing the city is that it is not ready for the fiscal independence it has been seeking. The District has been counting on continuing its traditional relationship with the Treasury while it tries to put its financial house in order.

In a letter to Rep. Ronald V. Dellums (D-Calfi.), chairman of the House District Committee, James M. Frey of the office of Management and Budget said the administration's intention is to " eliminate the Federal government as an unnecessary financial intermediator" and to "reduce the Federal involvement in local affairs."

To do that, he asked the committee for legislation that would push the city into accepting the fiscal independence of the Treasury, which has been anticipated since the Home Rule act was passed in 1973.

Specifically, Fey asked Congress to end interest-free short-term borrowing from the Treasury as of Oct. 1, 1983, and to require the Treasury to charge interest on any such loans made between that date and the time the law is passed.

OMB also asked Congress to limit to $155 million a year the amount of money the city can borrow long-term for capital improvements. Capital borrowing carries and interest charge, but Frey asked Congress to impose an additional half-percent surcharge on all loans.

In principle, the District government favors the idea of taking its capital borrowing out of the Treasury and into the bond market because the interest rates it would have to pay on tax-free bonds are lower than the rates it has to pay the Treasury.

But the city is seeking a two-year extension of its authority to borrow from Treasury because its financial advisers believe the District could not sell capital project bonds until its cumulative deficit is eliminated and its budget truly balanced.

Mayor Marion Barry and his financial counselor, Philip M. Dearborn, are out of town and could not be reached for comment.

An analysis of OMB's recommendations prepared by Jeff Humber, an aide to City Administrator Elijah B. Rogers, noted that the city "'as previously agreed" to the capital-borrowing limitation, but expressed concern about the proposed elimination of short-term borrowing power.

If "other sources were not available," Humber noted, the city could be left with "no source of short-term revenue."

The committee took no action on the proposals yesterday. Staff members said that the administration already has the authority to implement some of them, and that others might properly belong in other committees' jurisdictions