Jim Jarmusch’s Broken Flowers is the director’s most substantial film since Ghost Dog: The Way of the Samurai (1999) — a thriller about a legendary hit-man who negotiates his contracts by carrier pigeon. There is precious little of that lofty magic in Bill Murray’s suburban squat.

The wheels on Don Johnston’s life appear to have been stolen and replaced by piles of bricks. Like his washed-up movie star in Lost in Translation, Murray’s middle-aged bachelor seems to be stranded in emotional limbo. I love Jarmusch’s elusive heroes, but Murray’s stony-faced loner is a tough ask.

Dumped by his latest girlfriend (Julie Delpy), Don spends motionless days on the sofa, dressed in a shabby tracksuit, staring at his television set, and listening to classical music. For long, alarming moments, Murray has the implausible task of charming us with his catatonic daze.

The arrival of a pink letter from a mysterious former lover turns the key in the lock. It appears that Don has fathered a 19-year-old son. The author refuses to give her name. “Do I want to know? No, Winston, I don’t,” says Don to his happily married Ethiopian neighbour and keen amateur sleuth (Jeffrey Wright). Instead, Murray radiates that familiar sense of selfish isolation that afflicts almost all Jarmusch heroes. They have consciences like Teflon and a morbid fear of real life.

But Winston’s curiosity prevails, and armed with maps and plans, Don embarks on a road trip to track down and grill the potential suspects. Murray is his reliable deadpan best in a film that forces Don to peel back the past: a place full of former hippies, missed opportunities and old sores.

Sharon Stone is his first port of call, a widow with an over-sexed daughter called Lolita (Alexis Dziena) who walks naked around the house. He has an excruciating meal with Frances Conroy’s childless estate agent and her ghastly husband. Jessica Lange is wonderfully chilly as an upmarket “animal communicator” who squeezes him in between appointments with a neurotic pooch and a repressed rabbit. And Tilda Swinton’s trashy biker sledges Don mercilessly before her boyfriend knocks him out.

Jarmusch has rarely been so light-fingered. Every cringing encounter is pregnant with possibility. The joy is that the scenarios never play out as expected. The problem is that we don’t get enough of these feisty Juliets to feel any serious emotional traction. True, Don rediscovers what his life might have been like. Unfortunately, the memorable conclusion is “there go I but for the grace of God”.

The director is eloquent about the intimacy of strangers and surprisingly cruel about their shallow lives. I can’t help feeling that more, in this case, would be infinitely better.

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