Carne was married to actor Burt Reynolds from 1963 to 1965 and to producer Robert Bergmann from 3 May 1970 to 1971; both marriages were brief and childless, and ended in divorce. In 1978, after being found not guilty of possessing heroin, she was involved in a car accident along with her second husband; she recovered from a broken neck. Her drug problem continued and she was later arrested again for heroin possession. In 1986, she was arrested at London's Heathrow Airport and convicted of drug possession, serving two, of a three-months prison sentence in HM Prison Cookham Wood.