After serving in Iraq and Afghanistan, David Crowley began work on a spectacularly ambitious feature film called “Gray State.” As we learn in the new documentary “A Gray State,” Mr. Crowley’s movie was supposed to be a dystopian thriller designed as a warning against authoritarian control.

Mr. Crowley made a concept trailer that appeared online in 2012 and garnered a huge following. But despite signs of progress, the film never happened. Mr. Crowley was found dead in January 2015, along with his wife and daughter, in what police concluded was a double homicide and suicide: He had shot his family and then himself. Perhaps because Mr. Crowley was drawn to the paranoid fringe (he is shown meeting and watching Alex Jones), the deaths became a cause for conspiracy theorists.

The documentary’s director, Erik Nelson (a producer on “Grizzly Man”), explores the disjunction between the charismatic filmmaker-to-be with a penchant for both self-promotion and self-documentation and a man who was, it eventually seems clear, descending into mental illness. In one scene that captures the apparent duality of Mr. Crowley, the movie features an interview with two entertainment executives who speak enthusiastically about a meeting with him. Mr. Nelson then shows them as they listen to audio recorded beforehand in which Mr. Crowley describes plans to manipulate them.

There’s a morbid fascination inherent to documentaries like “A Gray State,” which is engrossing for the reasons it’s also unsatisfying: As Adam Shambour, a friend of Mr. Crowley’s, says, it’s a mystery that answers all the major questions except “Why?”