The baby sitter is none other than veteran Hollywood tough guy Tom Neal. A private detective, Neal is hired to keep an eye on the child of married couple George Meeker and Rebel Randall. Actually, Meeker and Randall are jewel thieves, and their "baby" is their stolen loot. Neal eventually catches on when he realizes that this is the quietest child on earth. Running a scant 41 minutes, Case of the Baby Sitter was designed to be shown in tandem with another Screen Guild Productions "briefie," The Hat Box Mystery: the films were shot back to back, with Tom Neal and Pamela Blake starring in both..