RENEE RICHARDS is, as most people know, a transsexual professional tennis player who used to be an ophthalmologist named Richard Raskind. As Renee Richards, she caused a furor in 1976 when she demanded to be allowed to play in officially sanctioned women's tournaments. Eventually, she got considerable publicity as the coach who helped Martina Navratilova become the top- ranked player in the world.

However, Second Serve has about as little in common with the standard tennis pro's autobiography as a psychiatric documentary on cross-dressing has with Tootsie. Only the final 70 pages of the book deal with Ren,ee's sensational appearance in the tennis world, and they are the least convincing chapters of the book. On the other hand, her account of Richard Raskind's first four decades adrift in a sea of gender confusion is bizarre and compelling.

Dick Raskind was born in 1934, the second child of two physicians. Their Queens household, as described here, was so crazy it would have driven most of us to the nuthouse, not to Yale, where Raskind went to college. His mother is portrayed as a cold, domineering psychiatrist who could not relate on any human level to her own son. His sister is shown as a tomboy who brutalized her kid brother and, with her mother, insisted on dressing him in girl's clothes. His father is portrayed as a distant shnook. (Late in the book, Dad is present at the circus- like first pro tournament Renee plays in. With a zillion cameras clicking, Renee walks over to him and he says, oblivious as always, "you still don't know how to hit those low balls.")

From the age of 6, Raskind lived a double life--or, to phrase it more correctly, a single life divided between two personalities. One was tall, handsome, heterosexual Dick, a compulsive overachiever who followed his parents' wishes by excelling in school and sports (he was a major league-caliber baseball player as well as a tennis star), first at New York's preppie Horace Mann, then at his father's alma mater, Yale, and finally at the University of Rochester Medical School. The other was Renee, the female persona he could not stop from emerging periodically, much to his own horror.

Dick loved beautiful women, rode a motorcycle, adored macho sports cars and served in the Navy. Ren,ee sneaked out of the house furtively in women's dress, went to transvestite nightclubs and sought for years to find a surgeon in the United States who would perform a sex change operation. In graphic detail, Richards tells how before her operation, she nearly mutilated her genitals with adhesive tape and other measures to achieve a smooth line beneath her panty girdle for her outings as Renee.

Despite 10 years of psychoanalysis, Dick failed to purge Renee from his system. Perhaps the most startling aspect of his story is how he managed to function successfully as an eye surgeon, medical scholar and administrator while the battle between his two selves raged inside. (One reason he could not find a U.S. surgeon to perform the sex-change for so long, he contends, was the medical community's fear of botching the job on such a well-known fellow physician.)

For many years before the actual sex change, Dr. Raskind took female hormones. They transformed him into almost a hermaphrodite: by day, a 6-foot male doctor with breasts, feminine curves and no beard, by night, a tall, rather elegant woman who sported a full-length mink. Dick/Ren,ee went through more than a few weird personality flip-flops. For instance, as a test, Dick spent several months in Europe as Ren,ee, in drag, where she was romanced by elderly Romeos and swinging Fellini-esque Italian couples. She contemplated having the surgery at a famous Casablanca clinic but chickened out at the last moment.

Dick's last stand before becoming Renee permanently was certainly a bravura performance. Upon his return to New York and doctoring, he met a gorgeous young woman with whom he fell instantly in love. Not only did she fall in love with him, too, breasts and all, but they got married and had a son. Eventually, Dick's neurotic behavior broke up their marriage, but not before he had --are you ready for this one?--breast reduction surgery.

Raskind finally found a surgeon who removed his male organs and substituted a serviceable female one. Everything you ever wanted to know about transsexuals --how painful the operation is, what sex is like afterward, what feminine changes occur--is here. Richards spares us nothing, and somehow her candor carries the tale along. There's no question that her gender identity problem caused her many years of anguish. Yet after she becomes Renee for good, her story loses some credibility.

Before the operation, Dick was flagrant enough to walk his dog in his Manhattan neighborhood dressed as Renee. Yet afterward, she gives up Dick's lucrative practice in order to move clear to California, where she tries to wipe out all vestiges of Raskind's illustrious career. She enters a partnership with an Irvine eye doctor at a fraction of the income she had once earned. She is intent on remaining anonymous yet defies all logic by playing competitive tennis at local clubs. What perfect irony that the Tennis-Battle-of-the-Sexes man himself, Bobby Riggs, is one of the first to recognize Ren,ee as the former Richard Raskind.

Richards says she put aside doctoring and decided to play the women's pro tennis circuit mainly because she was outraged at the requirement decreed by tennis officialdom that she take a chromosome test to prove her womanhood. Secondary, she says, was her desire to fight for the civil rights of transsexuals and her urge to enjoy a new career. Only the last reason rings true. It is also extremely difficult to believe her account of how her young son accepted Daddy's transformation into a second Mommy.

Billie Jean King deserves to have the last word on this most peculiar life story. During a doubles match, after enduring partner Renee's incessant whining about having the flu, King turned to the crowd and screamed, "This is the last time I'm ever playing with a Jewish American Princess!"