The District government's top money managers have a message for those who think they have been crying wolf about the city's financial crisis for the past year: The wolf is at the door.

In compliance with a court ruling that repealed the city's tax on suburban professionals, the District government will send out more than $33 million in tax refunds Wednesday.

Since there is no provision for the repayment in this year's budget, the funds are being diverted from tax revenues earmarked for other purposes which according to District officials make a serious cash crisis almost inevitable this summer.

City administrator Elijah Rogers and controller Alphonse G. Hill, in a joint interview, stressed in the strongest terms they have yet used that unless the city recives a major new infusion of cash by July, the city treasury wil be empty.

They said emergency measures, as well as what Hill called "fiscal calisthentics," may enable the city to keep meeting its payrolls and sending out welfare checks, but only at the expense of other obligations.

The District, like any other city, always has periods of cash shortages because its obligations, mostly salaries, are constant, but its revenues are sporadic.

The city usually is in a strong cash position in late March because the semiannual real estate tax collections that come in then tide the government over until the next collection in September.

This year, however, with $33 million of the March taxes diverted into the professionals' refunds, the city's cash obligations for the rest of the fiscal year are more than can be met either through tax revenues or through borrowing, Hill and Rogers said.

The two officials declined to make their cash-flow projection sheets public, on the grounds that no municipality or corporation does so, but Rogers produced a chart that he said illustrated the city's precarious position.

Measuring "demand liabilities," or bills currently due, against "cash and other assets," it shows that assets were twice as much as liabilities three years ago but now are less than liabilities.

If the creditors who hold those bills mostly federal agencies, demand immediate payment, Rogers said, "What are we going to do?"

Officials in the administration of Mayor Marion Barry have been predicting for nearly a year that the city's chronic devicits would finally develop by this summer into a critical cash shortage.

As the months rolled by and the city stayed afloat by laying off workers, deferring payments to suppliers and borrowing from the U.S. Treasury, skeptics suggested that the Barry administration was exaggerating or manipulating the budget crisis to bludgeon Congress into approving more financial aid.

Rogers and Hill made no secret of their exasperation at the reluctance of the public, the City Council, the press and members of Congress to believe that the city would actually run out of operating cash.

"We are serious. We have a critical situation," Rogers said. "Do we have to have payless paydays to convince people that there is a crisis? Only certain segments of the community say that, the ones who aren't dependent on city services. That's very dangerous talk."

"What do we have to do, shoot people to convince them about this?" Hill said. "It happened in Cleveland, it happened in Chicago, why don't people believe it here? We are saying it and the auditors' report shows it, so what does it take?"

The auditors' report to which he referred, issued on Feb. 1, showed that the District began this fiscal year last Oct. 1 with only $9.3 million in cash on hand and unpaid bills of $140 million. Many of those bills have since been paid as tax revenues have been received, but that meant using this year's revenues to pay last year's bills. Rogers, Hill and Philip M. Dearborn, financial advisor to Barry, said that the combination of the year-opening cash deficit and the professionals tax repayment makes it impossible to cover expenses for the rest of the year.

The professionals' tax, officially called the Unincorporated Business Franchise tax, was a levy on the income of doctors, lawyers, dentists and other professioanls who live in the suburbs and work in the District. It was struck down by the courts as a violation of a federal law prohibiting the city from taxing the incomes of non-residents, and the District is legally bound to repay it April 1.

As a liability that predates the start of the current fiscal year, the tax could be repaid out of the proceeds of a $184-million bond issue that Congress has been asked to authorize to enable the city to pay off its deficit from previous years, but Congress has not acted. In the absence of the revenue from the bonds, the city was obliged to dig into tax receipts to make the payment and to pay other back-year bills, leaving an inevitable cash shortage this year.

"In July we are going to have a severe [financial] drought," Rogers said. "We have to have that bond revenue or some other short-term money or else slow down expenditures so drastically that you can't do anything."

Rogers and Hill acknowledge that their comments amount to an unabashed plea for quick congressional action on the bond-issue proposal. But key members of Congress have expressed anger over indications that the District government, which over spent its budget by $105 million last year, will exceed its spending limit again this year. Hearings on the bond proposal are expected to be held in April.

According to Rogers, Hill Dearborn and other informed analysts of the city's financial affairs, the choices that will confront the Barry administration this summer -- if the bonds are not approved -- are all unpalatable.

Barry has declined to ask for further tax increases, pledged not to miss any payrolls or welfare checks and said he hopes to avoid any further layoffs beyond the 1,300 already imposed. That leaves these options:

Borrowing more cash from the federal Treasury. The District has unlimited authority to borrow interest-free, but such loans must be repaid within the fiscal year. The District has already borrowed $40 million this year. It could borrow more to get through the summer and repay the loan out of the September property tax collections, but that would only defer the crisis, Rogers said, because those September funds are earmarked for next year's operations.

Issuing "revenue anticipation notes," or short-term securities. The city could raise about $30 million that way, but the money would have to be repaid, with interest, in a year, which again would mortage next year's tax revenues to pay this year's expenses. Rogers said this course would be "completely irresponsible."

Deferring payment of bills to suppliers and canceling contracts. Hill said that undercuts the entire economy of the District and damages the city's overall credibility to potential investors if its bonding authority ever does come through.

"In the worst case," Rogers said, "we could borrow from the Treasury, not buy things, have another hiring freeze, cancel contracts and hold up on vendors. But how long can we keep on doing that? You ought to run the government in a well-managed way. Why should we have to juggle, finesse and delay payments?"

In the past, the District has borrowed from the Treasury at will and has saved cash by deferring tens of millions of dollars in payments to such lenient federal government creditors as the U.S. Bureau of Prisons, which bills the District for prisoners housed in federal institutions. But Rogers said the fiscal policies of the Reagan administration make it likely that federal agencies will soon tighten up on collections and put limits on Treasury borrowing.