You know you’re getting old when your favorite movie stars are starting to play characters afflicted with dementia. Arriving shortly on the heels of Knox Goes Away, featuring Michael Keaton as a hitman suffering from the condition, is Adam Cooper’s neo-noir thriller starring Russell Crowe as an ex-cop whose mental condition has deteriorated so dramatically that he’s forced to leave notes plastered throughout his apartment, Memento-style. Despite the plot element’s familiarity, it’s still the most intriguing element of Sleeping Dogs, a sluggishly rendered mystery that audiences will have long stopped caring about before it reaches its conclusion.

Crowe plays Roy Freeman, a former homicide detective whose sad state of being is immediately signified not only by those notes offering the simplest of reminders but also the stack of Hungry-Man frozen dinners in his freezer. He’s wearing a large bandage on his head, the remnant...