The Case of Jennie Brice by Mary Roberts Rinehart

The Case of Jennie Brice is a crime novel by the American writer Mary Roberts Rinehart (1876 - 1956) set in 1904 in Allegheny City, Pennsylvania (which since 1907 has been a part of the city of Pittsburgh).
It tells the story of a blood-stained rope and towel, and a missing tenant, Jenny Brice—all of which convince Mrs. Pittman that a murder has been committed in her boarding house. But without a body, the police say there is no case. Pittman tries to ferret out the killer by using the key to Jennie's apartment to investigate.