One style of mystery story popular in the early 60s (though there was the odd film even earlier, like Mahal) was the one where the suspense includes a seemingly supernatural element. A woman in white, singing a ghostly song of eternal yearning as she wanders half-seen (or unseen) through the gloom. Woh Kaun Thi?, Yeh Raat Phir Na Aayegi, Bees Saal Baad, Gumnaam, Raaz: all of them used this trope to the hilt.
As did this relatively lesser-known film [and you’ll probably realize, by the end of this post, why it’s little-known]. Poonam ki Raat was made by actor/writer/director Kishore Sahu, who played an important role in this film, the star of which was Manoj Kumar, quite a veteran of these suspense thrillers.