The Circular Staircase / Mary Roberts Rinehart

Rachel Innes is a spinster who has had custody of her orphaned niece and nephew since they were children. Halsey and Gertrude are now 20 and 24, respectively, and they talk Rachel into renting a house in the country for the summer. The first night Rachel is there, there is a mysterious trespasser and something falls down the stairs in the middle of the night. The second night, after Halsey and Gertrude have arrived, there is a murder, and Halsey and the friend he has brought to stay disappear. Halsey returns a few days later, without his friend and without an explanation, but by then many other developments have occurred, to the chagrin of the residents.