The 7th Victim
(1943)

Mary Gibson is called into the office at her private boarding school.  Mary is an orphan under the care of her sister Jacqueline.  Jacqueline has disappeared, and the school has not been paid in 6 months.  Mary goes to New York to look for her sister.  First, she goes to the cosmetics business their parents had left them.  The manager informs Mary that Jacqueline sold the business and may be traveling with the money.

Mary finds out Jacqueline had a secret room in a boarding house, but in that room they find only a chair with a noose hanging over it.  Mary takes a room in the same house, in case her sister comes back.  She learns that Jacqueline married without ever telling her, and meets the husband, Gregory Ward.  Mary gets a private investigator to search the cosmetics factory, but he is stabbed to death there.  They learn that the business was not sold, but given as a free gift to the manager.

It turns out that the manager of the cosmetics place is part of a devil worship cult, and she got Jacqueline to join.  As part of their pact, anyone who talks about it must die, and Jacqueline told her psychiatrist.  They are trying to force her to commit suicide, since none of them want to be responsible for murder.  They take Jacqueline to Mary's room in the boarding house.  When she is left alone, Jacqueline goes in the room with the noose and hangs herself.

With Jacqueline gone, Mary and Ward can admit they love each other.  (Which may be the creepiest part of the movie, since according to the story line she is still in high school and he is a lawyer who is already established in practice, much older than her.) 

Thanks Joseph C!