George Balanchine, who over the last six decades has choreographed over 100 ballets to the music of many composers, is now composing music--and lyrics--for a ballet to be choreographed by one of his dancers. The ballet will be danced by a horde of New York City policemen, some ballerinas and perhaps a politician in a boxing arena next month as part of a gala that has Nancy Reagan as honorary chairman.

According to the National Dance Institute (NDI), Balanchine--co-founder and artistic director of the New York City Ballet--will create a tango to be choreographed by Jacques d'Amboise and presented at the NDI's annual gala at Madison Square Garden's Felt Forum on May 24. D'Amboise, a principal dancer with NYCB, is also the founder of NDI, formed five years ago to offer free dance classes to children in the New York metropolitan area.

According to spokesman Sheila Tate, Nancy Reagan agreed to serve as honorary chairman because "she was so taken by" a performance staged by hearing-impaired children from the NDI program at the White House last December. Mrs. Reagan has no plans at present to attend the function, which will be filmed by NBC-TV for future telecast.

Balanchine's tango will be part of an approximately 20-minute-long ballet entitled "Fat City." The work will feature a group of New York City policemen who "study with d'Amboise to improve their stamina and coordination," NDI added. New York Mayor Ed Koch also has been invited to participate in the "Fat City" ballet.

Balanchine, 78, is known as an accomplished musician. (A brother who lives in the USSR is a famous composer there.) During the early years of the New York City Ballet, Balanchine occasionally conducted the ballet company's orchestra. In a little-publicized event, Balanchine also composed some music for a ballet presented at the NDI's gala last year.