As World War II slips from living memory, the question of how to preserve its legacy grows all the more vexing.

“There’s no old story that isn’t subjective somehow,” muses Akio Shimizu (Mitsuru Fukikoshi), the beleaguered protagonist of Ken Kawai’s “Headless Girl.” He’s the popular, not-quite-honest mayor of a provincial city, and all he wants to do is build a peace memorial.

Everyone loves peace, right? Yet this most unobjectionable idea sparks conflict with a local family that has found itself on the wrong side of history.