Memoir from opera star Domingo, Placido Domingo - My First Forty Years, by Placido Domingo. New York: Alfred A. Knopf. 192 pp. $15.95.

The story is told that while young Placido Domingo serenaded his sweetheart, a tin-eared neighbor called the police. ''What are you protesting about?'' screamed irate music-lovers, descending on the surprised complainer. ''You're getting a beautiful performance, free, by a member of the National Opera!''

This memoir is a collection of the ''more interesting details'' of the opera star's life, and a compendium of his opinions. For example, Domingo says that he is not over the hill musically. (''I know that I sing better, technically, artistically, than I did 10 or 15 years ago.'') He explains that he recorded pop songs with John Denver ''for people who do not enjoy opera.''

Domingo gives us not only a backward glance but a look ahead. Someday, he says, he'll sing in musical comedy and start an opera school where the most promising young singers and conductors will gain experience. Meanwhile, Domingo appears to be a man satisfied with his first 40 years, ''lucky and happy'' as he describes himself - as placid as his name.