The letter, accompanying new D.C. property tax bills, is headlined: "A Special Message from Mayor Marion Barry. " Coming from an official whos says he is "coming closer and closer" to a decision to run for reelection, the letter looks a lot like a campaign flyer.

After a greeting, in which the mayor seeks to head off any criticism for sending out an apparently political document in a regular city government mailing -- he contends that it saves on mailing costs -- Barry goes on to lay out the key message of his anticipated campaign.

It is the kind of message that voters could expect from an incumbent -- selectively optimistic descriptions of governmental initiatives for which Barry takes credit, like his crime program and his housing efforts, with no mention of areas in which his administration has failed, like the still-chaotic water-billing system.

He mentions popular officials and trends for which he has no responsibility, like D.C. schools Superintendent Floretta D. McKenzie and the downtown construction boom. And then, in a flagrant example of what might be called incumbentspeak, Barry tries to soothe the taxpayers' ire at property tax bills that have risen this year an average of 21 percent.

"Even though several of my staff recommended a tax rate increase," Barry writes, "I have decided to hold the line on the property tax rate." The image of Barry struggling valiantly against his own staff seems to ignore the fact that the staff members serve at Barry's pleasure.

As if these weren't enough clues that Barry is running hard to remain in his red leather chair, he throws in some pointed praise of City Council Member John A. Wilson (D-Ward 2).

In a recent housing ceremony in Wilson's ward, Barry also had fulsome praise for Wilson. Several months ago, though, the two men were at each other's throats over what Wilson perceived as a double-cross by Barry. The episode began when the mayor suggested a drastic increase in D.C. death taxes, which was adopted by the council and then quickly repealed in the face of strong protest. Barry then disowned the legislation, leaving Wilson, as head of the council's finance committee, holding the bag.

Barry's sudden warmth toward Wilson results, District Building sources say, from his fear that Wilson might run for mayor himself or support someone else. Wilson is considered popular among his constituents, and could possibly deprive Barry of needed support in Ward 2, an area where Barry is traditionally strong. But Wilson, so far, has made no commitments. "We are amused," an aide to the council member said.

Meanwhile, Barry is busy trying to demonstrate that he has broader support than other potential candidates. He was weak in the 1978 primary among middle-class black voters. But he took a reporter aside earlier this week and showed him a computer printout of the results of the primary election three years ago. Barry cited selected precincts -- Pct. 62, for example, in the northern tip of the city; and the precinct containing his home in Southeast, which has seen an influx of middle-class blacks -- in an attempt to demonstrate that he held his own against Sterling Tucker and Walter E. Washington among these voters. (The totals showed that he, indeed, held his own in the precincts he picked, but did not win them.)

Add to that Barry's recent pattern of public appearances and his lunches with 1978 supporters, like a Madison Hotel repast a few weeks ago with campaign advertising man David Abramson, and you get a picture of a politician who's running for something.

Meanwhile, scads of other potential candidates continue to make political noises: Wilson, council Chairman Arrington L. Dixon, council members Betty Ann Kane and John L. Ray, former council chairman Sterling Tucker. The profusion caused Flaxie Pinkett, one of the politically active Washingtonians whose support is being courted, to sigh recently: "Now they all want to bring me their polls so I can see them."

Don't wait for the mayor's race to begin. It already has.