Boyle's Dilemma by T. C. McKeon

When upper-class Englishman Robbie Templeton is murdered in Chicago, his sister Alice, finding the Chicago P.D.'s lack of interest in the case appalling, enlists the help of private detective Tim Boyle. Embarking upon a search for the killer, the trail leads Alice and Tim to South Dakota, where Templeton worked as a missionary to the Sioux, then back to Chicago—where the web of danger grows tighter and tighter around them…