Death of an angel (1952)

The angel of the title is Jane Baxter, the wife of country physician Patrick Barr. Everybody in the small British village where she lives thinks the world of Baxter; thus, when she is murdered, the authorities are out for blood. Dr. Barr seems above suspicion, at least until he begins behaving eccentrically. As time passes, most everyone learns that Baxter wasn't quite as angelic as she seemed-and that quite a few people might have wanted her dead.