This makes for a very intriguing mystery! I especially like that Constance Ford, generally a character actress, gets to play sexy for once. Dowdy Helen Reed is also 'ball of fire' Joyce Martel, the beloved of tough-guy nightclub owner Johnny Hale. Her dual personality creates some lively complications-- is she two-timing anyone? Her doctor finally weighs in with the facts on Helen/Joyce, erroneously referring to her condition as Schizophrenia; any doctor would have known better.
Multiple Personality Disorder or Dissociative Disorder, now known as Dissociative Identity Disorder, had been first identified in the 1880s, but has still remained largely a mystery to many people. It has often been confused with personality shifts symptomatic of some forms of schizophrenia, giving rise to widespread misuse of the term 'schizophrenic' to indicate a 'split personality' or to express general duality. Schizophrenia is a psychosis, a mental illness treatable with medication, while Dissociative Identity is an acquired personality disorder usually formed as a survival mechanism after unbearable trauma.
The idea of split personality has readily leant itself to dramatic portrayal, especially onscreen, and this has served to familiarize more of the general public with the condition. There was Blanche Sweet in "The Case of Becky" (1915) from the stage success by that name, remade in 1918 as "The Two-Soul Woman" with Priscilla Dean. Still to come were Constance Binney in a remake of "The Case of Becky" in 1921, followed by Gladys Walton in "The Untameable" (1923). Barbara La Marr took on a new treatment of the theme in "Sandra" (1924). More familiar today after 1957's "The Three Faces of Eve" would be small-screen treatments "Cybil" with Sally Field, and Shelley Long in "Voices Within: The Lives of Truddi Chase". But use as a dramatic device is quite widespread. 2001's "K-Pax" even throws in an extraterrestrial twist, and "The Danish Girl" from 2015 complicates matters with a transgender issue.
"Deadly Double" is definitely worth a look.