Love Has Many Faces

Love Has Many Faces is a 1965 American drama romance film directed by Alexander Singer, and written by Marguerite Roberts. Nancy Wilson sings the title song and Edith Head designed Lana Turner's clothes.
Plot.
When a dead American "beach boy" is washed up on a beach in Acapulco, the police do an investigation to see if it was murder. Lieutenant Riccardo Andrade (Enrique Lucero) of the Mexican police interviews three suspects. Hank Walker (Hugh O'Brian) is another beach boy who works as a gigolo and also blackmails vacationing middle-aged American women. Pete Jordan (Cliff Robertson) is a former beach boy who married rich American Kit (Lana Turner). Kit met Pete when he was selling his blood and bought all of him. The dead man was wearing a bracelet engraved "LOVE IS THIN ICE," which the police discover was given to him by Kit. They also discover that he'd had an affair with her.
In addition to the police, the dead American's deserted girlfriend, Carol Lambert (Stefanie Powers), comes to Mexico to find out about her former boyfriend's death.