Storm clouds pass over a soybean field near Salem, South Dakota. The state lacks a film tax credit, prompting many productions to go elsewhere.

Director Kate Beecroft spent three years living with a family in South Dakota before she started writing a script about their lives.

Last month, 1,100 theaters across the country showed a movie ostensibly set in rural South Dakota. The film, “Americana,” features Sydney Sweeney as a small-town diner waitress on the hunt for a rare ...