In Washington, where three-fourths of the registered voters are Democrats, local Republicans have been well-advised to approach citywide elections fatalistically.

In the 1978 mayoral election, for example, Republican Arthur A. Fletcher, a former assistant labor secretary in the Nixon Administration, ran against Marion Barry, who had won the Democratic nomination with a mere 35 percent of the vote in a bitter primary. Fletcher made an impressive showing by GOP standards, mustering 28 percent of the vote in the general election.

With the next election for mayor less than a year away, the loosely knit, outgunned D.C. Republican Party has been salivating over the possibility that Vincent E. Reed, the popular former D.C. school superintendent, might be coaxed from his post with the Reagan administration to carry the party's banner.

A Washington Post poll conducted a year ago suggested that Reed, a back-to-basics educator and a decisive, no-nonsense administrator, was more popular than Barry and a field of potential mayoral candidates.

"If Vincent Reed were to run for mayor, he would be a very viable candidate," said D.C. Republican chairman Robert Carter. "As a matter of fact, I think he could win. . . . I think this town is ready for that kind of integrity."

City Council Chairman Arrington Dixon, a Democrat who is pondering a challenge to Barry, believes Reed -- who as a Republican would be spared the predictably bitter and expensive Democratic primary -- might be tough to beat in a general election.

"I think Vincent clearly has tremendous name recognition, he served the city well, he has a lot of supporters and he'd be a viable candidate for any office in the community," Dixon said. "But his intent is important -- whether he wants to run."

Until now, Reed has given few, if any, visible signs that he plans to leave his $52,750-a-year post as an assistant secretary in the U.S. Department of Education to enter local politics.

He didn't attend the D.C. Republican Party's fall fund-raiser last week at the University Club. Nor has he spoken with Carter or Michael Gill, chairman of the local Republicans' candidate selection committee.

"I assume overtures will be made to him," Gill said last week.

Never mind, Mike, Reed suggested this week. "At this time, I'm not interested in running. . . . I don't anticipate changing my mind. I don't want to be mayor," he said. "I'm not a politician."

Reed said he gladly would have told someone in the Republican Party about his decision, but "No one asked me."

If Reed sticks by those sentiments it would be at least a rhetorical setback for Barry, who has already been trying out a potential campaign pitch that would link Reed to the administration that sharply reduced federal aid to urban areas -- like Washington.

"He works for Reagan," Barry said this week. "I'm not going to worry about him."

But so far, there is no Vince Reed to kick around. The only Republican to declare his candidacy for mayor to date is political newcomer James E. Champagne, 38, a free-lance writer who formerly worked for the American Petroleum Institute and the Chrysler Corporation -- a virtual unknown to Barry, and to the local GOP as well.

Last summer, Mayor Barry sent out with D.C. property tax bills some letters that strangely resembled a camapaign flyer.

"Even though several of my staff recommended a tax-rate increase," Barry wrote, "I have decided to hold the line on the property tax rate."

Well, the mayor is at it again. This time, it's a letter sent out on official District of Columbia stationery and dated Dec. 4 inviting citizens to attend one of several public meetings he is holding around the city.

"It has been almost three years since I took office as the mayor of one of America's greatest cities," the letter begins. "During this time, I have tried to bring sensitive, competent, honest and responsible leadership to the mayor's office."

Barry contends in the letter that he can't be held responsible for all of city government's problems, since more than one-third of the city's employes -- chiefly those who work for the school system -- are not under his direct administrative and legal control. He goes on to outline what he considers his most impressive accomplishments, before concluding:

"The record is positive, but I have had to make some unpopular and tough decisions, too. There is still much to be done."