Richards was born Richard Raskind on August 19, 1934, in New York City, and was raised, as she put it, as "a nice Jewish boy" in Forest Hills, Queens. Her father David Raskind was an orthopedic surgeon, and her mother was one of the first female psychiatrists in the United States, in addition to being a professor at Columbia University.
Richards attended Horace Mann School and excelled as the wide receiver for the football team, the pitcher for the baseball team, and on the tennis and swim teams. Richards's baseball skills even led to an invitation to join the New York Yankees, but Richards decided to focus on tennis. After high school Richards attended Yale University and was captain of the men's tennis team, and was considered by some to be one of the best college tennis players in the country. After graduating from Yale, she went to the University of Rochester Medical Center and specialized in ophthalmology, graduating in 1959 and serving a two-year internship at Lenox Hill Hospital in New York. After an internship, Richards served two years of residency at the Manhattan Eye, Ear and Throat Hospital in New York. Richards played competitive tennis for a while and was ranked sixth out of the top 20 males over 35. After an internship and residency, Richards joined the United States Navy to continue medical training and played tennis in the Navy. While serving in the Navy, Richards won both the singles and doubles at the All Navy Championship, with a very effective left-hand serve. During this time Richards was ranked as high as fourth in the region.
During college Richards began dressing as a woman, which at the time was considered to be a perversion, and transsexualism was classified as a form of insanity. Richards named the female alter ego Renée, which is French for reborn. This struggle with sexual identity created sexual confusion, depression, and suicidal tendencies. Richards began seeing Dr. Charles Ihlenfeld, disciple of Harry Benjamin who specialized in endocrinology, transsexualism, and sexual reassignment. Upon seeing Dr. Ihlenfeld she began getting hormone injections with the long-term hope for a life change. In the mid-1960s she traveled in Europe dressed as a woman, intending to go to North Africa to see Georges Burou, a famous gynecological surgeon at Clinique Parc in Casablanca, Morocco, regarding sex reassignment surgery; however, she ultimately decided against it and returned to New York. Richards married model Barbara Mole in June 1970, and together they had a son Nicholas in 1972. They were divorced in 1975. In the early 1970s, Richards resolved to undergo sex reassignment and was referred to surgeon Roberto C. Granato, Sr., by Harry Benjamin, successfully transitioning in 1975. After surgery, Richards went to Newport Beach, California, and started working as an ophthalmologist in practice with another doctor.
Following Richards' disclosure of her gender reassignment, the United States Tennis Association (USTA), the Women's Tennis Association (WTA), and the United States Open Committee (USOC) required all women competitors to verify gender with a Barr body test of their chromosomes. Richards applied to play in the US Open in 1976 as a woman but refused to take the test, and thus was not allowed to compete in the U.S. Open, Wimbledon, or the Italian Open in the summer of 1976.
Richards then sued the USTA in New York state court, alleging discrimination by gender in violation of the New York Human Rights Law. She asserted that participating in the tournament would constitute "an acceptance of her right to be a woman." Some USTA members felt that others would undergo sex change to enter women's tennis. Sports Illustrated called Richards an "extraordinary spectacle", and characterized reactions to her as "varying from astonishment to suspicion, sympathy, resentment, and more often than not, utter confusion." The USOC stated "there is competitive advantage for a male who has undergone a sex change surgery as a result of physical training and development as a male." Richards finally agreed to take the Barr body test. The test results were ambiguous. She refused to take it again and therefore was barred from play.