The 2010 murder of two Arkansas police officers by an anti-government father and son serves as the basis for “Sovereign,” a grimly gripping new movie. With an intelligent, judicious script and assured filmmaking, writer/director Christian Swegal surmounts not only the feeling of redundancy often found in true crime depictions but also the modest qualities expected of a directorial debut. Arguably the filmmaker’s smartest decisions relate to his choice of actors, particularly Nick Offerman and Dennis Quaid, who give powerful performances.

The casting of Mr. Offerman, in particular, was a shrewd one, as it allows “Parks and Recreation” fans to envision how his affectionately gruff, libertarian sitcom character’s life may have unfolded had his life taken some tragic turns and setbacks, and had he not worked as a city official in Pawnee, Indiana. The real-life Jerry Kane, whom Mr. Offerman portrays, even ran three unsuccessful races for the city commission at Springfield, Ohio. 

Kane’s later life, though, reads nothing like a sitcom: Working as a trucker in the late 1990s, he experiences a terrible tragedy when his infant daughter dies of SIDS; an autopsy was performed against his wishes, which likely contributed to his ire at authority. Sometime afterward, Kane starts to espouse the ideology of “sovereign citizens” and individual rights, while believing he no longer needs a driver’s license. The family home goes into foreclosure twice, and a few years later, his wife dies. Indictments on forgery and theft charges and traffic arrests coincide with his setup of a seminar business based around debt avoidance at the height of the mortgage crisis in 2008.

The movie picks up the account of Kane’s life in the months leading up to the shooting in 2010. In opening scenes, we see Kane’s teenage son Joe (Jacob Tremblay) alone at home, where large guns rest casually in corners. A knock at the door is yet another foreclosure notice delivered by a bank representative and a cop. Later in the evening, after Kane arrives back from one of his seminar tours, the father participates in a radio talk show as an expert on foreclosures and deeds of trust while the boy plays a violent video game.

In these early scenes, Mr. Swegal could be accused of leaning into the poverty of the setting and Kane’s irrationality, yet there’s no trace of condescension in the depiction of the paternal and filial bonds. When Kane quizzes his homeschooled son on social studies, we witness subtle tenderness and respect between the two, even when the elder ends up cryptically discussing how his own father once spoke of a grand conspiracy.

After Kane has a combative exchange with a clerk at the local recorder office over an “affidavit of truth” — with Joe filming the encounter and looking embarrassed — he lectures his son again about rights, though the boy has clearly heard it all before. Soft-spoken and a bit cowed, Joe appears to be chiefly at odds with his dad’s demeanor and way of thinking, which is one element in which Mr. Swegal departs from eyewitness accounts. Primarily told from Joe’s perspective, the drama presents us with a Joe Kane who would rather go to school, have his father pay the mortgage, and hang out with the neighbor’s daughter than go along with his father to his seminars, which he eventually does. 

As portrayed by the young Mr. Tremblay (“Wonder”), Joe is heartbreakingly awkward, what with his lanky body and uneasy attempts to reconcile the love for his father with his own developing, questioning views of the world. The issue with this interpretation, though, is that Joe never displays any signs of volatility, such as during a deranged duel scene instigated by his father, causing the shocking violence that he later instigates to appear both abrupt and inconsistent with the character. Mr. Tremblay certainly looks the part of a gawky, impressionable 16-year-old, but his acting relays very little of the screenplay’s intimations of trauma and pent-up anger and anguish.        

As Kane, Mr. Offerman has a few scenes in which he humanizes the unstable, unprincipled man, but unlike with Joe, we’re never meant to identify with him, even if his talk of institutional overreach occasionally judders with truth. Kane’s debt seminars, in which the actor leverages his trademark relaxed yet contemptuous voice, contain a smattering of information but largely consist of basic sarcasms and common gripes. Audience members don’t seem to mind, though, with some left “inspired,” even when his statements turn increasingly bellicose.

Prompted by the fact that one of the victims had a father who was chief of police, Mr. Swegal gives us an occasional look at the life of one of the murdered officers and his boss/father, balancing his portrait of the perpetrators. Mr. Quaid plays the police chief with a tough-love intensity that both contrasts and connects with Kane’s extreme pronouncements and indoctrination of Joe, deepening the director’s exploration of fatherhood and filial independence. Ultimately, it’s Mr. Quaid’s stunned face and locked jaw near the film’s end that provides its most haunting image — a devastating glimpse at profound loss.