In Greenwich Village, `Mayor (the Musical)' is doin' fine. Mayor (the Musical) Revue with music and lyrics by Charles Strouse, book by Warren Leight. Based on ``Mayor,'' by Edward I. Koch. Directed by Jeffrey B. Moss.

Mayor Edward I. Koch wouldn't be Ed Koch without his trademark question: ``How'm I doin'?'' For ``Mayor (the Musical),'' Charles Strouse has posed the question in song. The answers his honor (Lenny Wolpe) receives from several constituents on the stage at the Top of the Gate might daunt a lesser man. But not our Ed. He takes them in jaunty stride. Which is just one of the reasons for reporting that down in Greenwich Village, Mr. Koch's own neighborhood, ``Mayor (the Musical)'' is doin' fine. Mr. Strouse and sketch writer Warren Leight attribute their collaboration to ``Mayor,'' Mr. Koch's best-selling autobiography. Actually the adaptors have used the Koch memoir as the launching pad for a predominantly good-natured spoof of New York City's chief executive, some of his allies, some of his opponents, and some of the rest of us. If Ed Koch is the quintessential New Yorker, ``Mayor (the Musical)'' is essentially New York-y.

The show open with some radio bulletins from the PA system about a mass escape form the Bronx Zoo -- the comic import of which got rather muffled in the amplification. No matter. ``Mayor'' is quickly on its tuneful and topical way. There are songs and sketches about such matters and personalities as the city's Board of Estimate, Harry and Leona Helmsley (Keith Curran and Ilene Kristen), New York's royal couple of real estate and hostelry; urban Yuppies; and political coalitions that don't coalesce. In ``Hootspa,'' the mayor defines ``chutzpah'' to predecessors John V. Lindsay and Abe Beame (Mr. Curran and Ken Jennings). If my notes can be trusted, Mr. Koch rhymes nerve and verve with ``throwing a curve.''

The Leight sketches include ``Alternate Side,'' in which Kathryn McAteer discourses on a life dedicated to finding a parking space, and ``On the Telephone,'' simultaneous conversations in which Mayor Koch and council president Carol Bellamy (Miss McAteer) reach more or less the same conclusions about each other. Among the more amusing numbers are ``I Want to Be the Mayor,'' with Comptroller Harrison Goldin (Douglas Bernstein) lamenting forever being second man; ``Subway,'' which includes ``The Last `I Love New York' Song,'' and ``Good Times,'' which assembles John Cardinal O'Connor (Mr. Bernstein), Bess Myerson (Nancy Giles), the ubiquitous Helmsleys, and David Rockefeller (Mr. Jennings) for a salute to Koch. For a contrastingly darker touch, ``We Are One'' partners Harry and Leona with two homeless street people (Marion J. Caffey and Miss McAteer) in a short, bitter pantomime.

Without attempting actual impersonation, Mr. Wolpe catches Koch in the essentials -- the high-pitched voice, the energy, bravado, and verve. In the fashion of such entertainments, the rest of the performers play multiple parts. The cast is nimble and versatile. Credits also go to musical director-arranger Michael Kosarin and his excellent combo, choreographer Barbara Siman, set and costume designer Randy Barcelo, and lighting designer Richard Winkler. Jeffrey B. Moss has directed with panache and maybe even with chutzpah.

To help out-of-towners -- and probably a few New Yorkers -- the management has provided a glossary of more than 40 names and terms encountered in the course of this diverting New York political digest. Whether or not Koch (the mayor) deserves to be reelected, ``Mayor (the Musical)'' deserves to run.