The Unkept Woman by Allison Montclair

Business is good for the owners of The Right Sort Marriage Bureau (Mrs. Gwendolyn Bainbridge and Miss Iris Sparks), but they are dragged into solving a murder once again when a dead body--first assumed to be Iris--is found in Iris' apartment. In order to clear her name, Iris, along with a very reluctant Gwen (who is trying to gain back custody of her young son and needs to be above reproach) try to uncover the murderer. Another very enjoyable entry in the Spark and Bainbridge series.