Black-white movie about transvestite?

In the fifties or possibly the sixties- allowing for television reruns- there was a movie or TV crime drama that was about a Transvestite or Latent Homosexual. It was in the context of the missing witness angle of a crime drama. it so transpired that the character was a biological male who had been, in the polite phrase of the time- been ( Raised as a girl) and wore female costumes, etc. Even then the idea seemed to be not only was /is Homosexuality ( wrong) it is, of course, but you had to blame somebody and it seemed to be the (parents wanted to have a girl child). I think this is the film you are referring to. a biographical film- probably in technicolor was done on the Christine Jorgensen story- that being the title of the film in the seventies. Nuff said.