First, I have a HarperCollins copy of this book in softcover, published in 1994, 5" x 8", 157 pages. The work was originally published in 1964.
While the saga is slated as a "mystery," and murder does in fact ensue, this story just doesn't fall into the arena of Christie, Rinehart, or even previous Ellery Queen. It's more like a "Cadfael" entry.
A contemporary guy is transported back in time (spiritually speaking) when he gets stranded, and drawn into, an isolated religious community in the American southwest. These folks have existed for generations, virtually unknown to the outside world, only sending out one or two members for necessary supplies once in a great while to a small general store which is located in the desert boondocks. Think "The Village," The Village (Widescreen Vista Series).
Our protagonist interacts with these people and finds himself in the position of "investigator," when a murder occurs amongst the flock. Why does he feel compelled to solve the mystery? Because these pious folks have their own VERY unusual justice system, (which is also a bit rusty from lack of use), and the wrong guy might just be getting tagged for this one.
Folks, this is a very compelling tale, albeit an all-too-short one. In any case, it's a page-turner. Highly recommended.