Who Killed the Tall One in the Middle?

The lead singer in a sister trio act is poisoned. Both the surviving sisters hated the victim, but others had motive as well: the nightclub owner, the trio's former arranger, the girls' agent, their stepfather, and a real estate agent who had been involved with two of the sisters. After one of the suspects is attacked and brutally beaten, Tim is nearly run down by a speeding car and another suspect is murdered. Burke finally discovers the solution to the crime at a sanitorium.