Joe May might as well be dead. Heck, almost everyone already thinks he’s left this mortal coil.

The Last Rites of Joe May,” on DVD April 17, follows an aging hood trying to piece together his life after a long hospital stay. It’s a serially depressing tale of a man whose poor choices derailed his chance for happiness.

Even by Ralph Kramden’s get rich quick standards, Joe May is delusional to the core.

And yet the man charged with playing Joe can bring dignity to the saddest of sacks. Character actor Dennis Farina never lets Joe seem like a fool. The old man knows he’s made a mess of things, but he’ll be darned if he’s going to show it. He just tugs tighter on his leather jacket, oblivious to both the Chicago chill and his waning list of options.

Writer/director Joe Maggio supports Farina’s solemn work by transcending plot points you’ll spot long before they take shape.

The film opens with Joe leaving the hospital after a protracted bout of pneumonia. While he was away his landlord junked his meager possessions and his car got sold for a whopping $75. Joe’s life savings will only cover him for a few weeks, if he’s lucky.

When Joe lucks into sharing an apartment space with a single mother and her curious daughter (Jamie Anne Allman, Meredith Droeger) it could be his last chance to make the right choice. But is he too self-absorbed to see the opportunity before him?

“Joe May” oddly parallels 2010’s “Crazy Heart,” both with its deeply flawed main characters and their inability to square away their demons. Joe’s pride prevents him from taking the easy way out. When he tries to reconnect with a local mobster (Gary Cole, oozing insincerity and malice), the results are as darkly comic as any scene you’re likely to watch. Even at its peak, “The Sopranos” couldn’t hit such a maudlin note.

It’s a minor miracle Joe connects with the single mother’s daughter, a plot device that wouldn’t work at all without Farina’s effortless posture. He’s got just enough heat on his old fastball to charm the lad without even really trying. Farina made his name playing tough guys, men who get their way with an angry glare or an aggressive pose.

Here, it’s like those essential skills have slowly wasted away, leaving the attitude with little to back it up.

“The Last Rites of Joe May” ends on such a beautifully somber note, you’ll keep staring at the screen as the credits roll. The spell Farina casts for 90-odd minutes won’t fade to black that easily.

The DVD includes outtakes as well as an interview with writer/director Maggio.