The District government, currently running a $59 million deficit, plays host to its very first city-sponsored marathon this Sunday, dipping into its pockets to pay $47,000 in overtime 350 police officers to be on hand for the event.

Private donations and more than 1,000 volunteers will cover most of the marathon's cost, but the city will still provide several other services, the exact cost of which city officials could not determine yesterday.

The gaggle of 900 gym-suited runners will pount out the 26.2 miles of the ragged, circular course on streets that will be freshly swept by the city's department of environmental services and will have their times recorded on computers run by the city's university.

But the race, modeled after the famous Boston and New York marathons, will be well worth the money, said William H. Rumsey, director of the city recreation department, which organized the event. The race is aimed at a wide range of local residents -- people from age 13 to 73 have registered -- and will inspire pride in the city among local residents, Rumsey said.

The recretation department "has not spend one dime" on the race other than using employes working normal hours, Rumsey said. The volunteer services and donated goods for the race would cost "several hundred thousand dollars" if the city had to pay for it all, he said.

The runners, 765 men, 72 women -- 96 percent of them from the Washington area -- will step off at 8 a.m. from a staging area on the mall where three commercial sponsors, who have donated more than $30,000 of the $50,000 in private funds collected for the event, will give runners promotional gimmicks such as logo-laden than three dozen firms, civic groups and indivuduals contributed most of the remaining $20,000. Runners paid $5 each to enter.

Rumsey's recreation department has been one of the hardest hit in Mayor Marion Barry's budget cutting efforts, laying off more than 150 employes this year and getting by with a permanent staff of 443, down from 772 just over a year ago. But Rumsey said no recreation program is being cut to help pay for the race.

Sam Jordan, director of the command center for the Office of Emergency Prepardness, said his employes, who provide a coordination center during public events in the city, are volunteering their time for Sunday's run.

The marathon comes one week before the famous Boston Marathon which attracts 6,000 runners and follows by only a week the annual Perrier Cherry Blossom Classic 10-mile race.

Recreation officials did not consult area running clubs when they initially began planning the marathon, causing some ill feelings between the officials and the clubs, who said the race is too soon after last week's Perrier race and too close to the Boston run.

Rumsey said many of the critics are "jealous" that the city is "pulling this off."

The route will begin at the mall and will cross 281 intersections and pass through the Northwest enclaves of Georgetown and Cleveland Park. It will cross Rock Creek Park and pass through the neighborhoods of Adams-Morgan and Mount Pleasant in Northwest Washington and move on through the Northeast neighborhoods of Brentwood and Brookland and Anacostia and Fort DuPont in Southeast. The race will end where it began, on the mall.

"That's what it's for," Rumsey said, "to show the whole city."