The Case of the Perfect Maid = The Maid Who Disappeared — Agatha Christie

When her maid asks Miss Marple to intervene in the delicate problem of her rather opinionated cousin Gladys, she doesn't think much can be done. Poor Gladys has been accused of stealing a precious brooch belonging to her employers, the reserved Misses Skinner. While one sister malingers with mysterious ailments, the other attends to her every need, and they've both decided that Gladys must go. But, one day there appears a paragon to replace her, the perfect maid, or so they think….