WHO IS going to pay the cost of overtime for District policemen involved in the evacuation of the Iranian embassy? You'd think it would be the U.S. government. After all, the Iranian diplomats were not accredited to the District of Colubmia, and it was President Carter; not Mayor Barry, who ordered Iranian diplomats to get out. But nothing is self-evident when it involves the sometimes touchy relationship between the federal and District governments. For instance, when the pope ended his visit to the United States with a stop in the nation's capital, the federal government did not pick up the $642,731 tab to pay city workers for controlling crowds, leading motorcades, and so forth. Similarly, the Office of Management and Budget said it would not pay the city for the $86,000 in police overtime resulting from a demonstration against the shah in December. And now the financially poor District government is about to get a bill of yet undetermined size for the cost of police work involved in closing off Massachusetts Avenue near the embassy and helping federal authorities to watch the embassy and get Iranian diplomats to the airport.

The argument over whether the District or federal governemnt should foot the bill for large demonstrations and the costs incurred by visits of dignitaries is supposedly resolved by the District charter. As approved by the Congress six years ago, the charter says that the federal government is obligated to repay the city for "necessary expenses incurred by the District in connection with assemblatures . . . which relate primarily to the federal government." This payment is to come to the District apart from the annual payment the federal government makes to the District for land occupied by the government (tax-free) and for the small, everyday marches, protests and problems that are generated by a city that is also the nation's capital and that are handled by city workers.

But it is not only the issue of paying for special services that creates bad feeling between the federal and District governments. Even the annual federal payment to the District is unpredictable in size and subject to long, sometimes angry negotiations between city officials -- hungry for any dollar they can get -- and Congress -- anxious to show the folks back home that they can control government spending.

The federal government should be chipping in somehow for bills attached to the presence of District policemen at the embassy for two days, the pope's visit and the policing of anti-shah Iranian demonstrators. But even the full federal payment has not been paid to the city this year.

President Carter said Tuesday that he supports giving the District the full payment. But Congress is balking. Congress should follow the president's recommendation. And while Congress is on the subject of payments to the city, it should clarify the federal government's financial responsibility for international and national events that use city services. The current law is apparently not enough to get the federal government to pay its proper share of the bills.