Door between Devil

From Wikipedia: "Karen Leith is a novelist whose fictional life and works bear a resemblance to Pearl S. Buck—she was raised in Japan and writes novels that are set there, but lives in Manhattan surrounded by Japanese customs, art and furnishings. She is engaged to marry world-famous cancer researcher Dr. John MacClure. One day, the doctor's daughter, Eva, finds Karen with her throat cut in the writer's Washington Square home. Eva herself has no motive to kill Karen, but the evidence she finds at the scene suggests—even in her own mind—that no one else could have done it. The investigation by Ellery Queen confronts this puzzle and also turns up startling information about a long-vanished relative of Karen Leith. Queen pierces the veil of circumstantial evidence and finds out not only the method of the crime but, most importantly, its motivation."