Laurie Anderson’s “Heart of a Dog” is a dreamy thing, part doc, part memoir, part meditation, in which the dauntingly multidisciplined artist (painting, sculpture, poetry, music, moviemaking) celebrates the life of her beloved rat terrier, Lolabelle, mourning her death and honoring it, too.

Incorporating old 8-millimeter home movies, staging re-enactments of childhood events, quoting Kierkegaard and noting how the Department of Homeland Security’s cautionary catchphrase, “If you see something, say something,” sounds like it was written by philosopher Ludwig Wittgenstein, Anderson explores spiritual and physical dimensions — and the points where they might intersect.

Anderson, who actually had a Top 5 hit single in the U.K. way back in 1981 with the half-cooed, half-recited “O Superman,” narrates “Heart of a Dog” in a breathy timbre that’s forever in danger of sounding precious, rather than perspicacious.

But if you can get past that Meditation 101 instructor vibe, “Heart of a Dog” functions to illuminate the connections between art and life, human and beast, memory and imagination, between the loved ones in your life and the people you can’t bring yourself to love.

The ashen debris of 9/11, the falling bodies, the fearful aftermath of the Twin Towers attack figure in Anderson’s consciousness — and in her film, too. The performance artist’s Greenwich Village apartment looked out onto the Hudson River drive where trucks carried away the broken steel. Escaping to the hilly coast of Northern California, Anderson spends her days in the company of Lolabelle; when predator birds swoop down close to her small dog, the look of fear in Lolabelle’s eyes reminds Anderson of the way New Yorkers walked around, staring skyward, edgy in the days after the World Trade Center disaster.

Lou Reed, Anderson’s companion for decades, shows up fleetingly in “Heart of a Dog,” playing a doctor in a hospital scene. The singer and musician died two years ago. His lovely, loping “Turning Time Around” ends the film — a film Anderson dedicates to his memory.

In her voice-over, Anderson says that crying is not permitted in the Tibetan Book of the Dead. And she quotes David Foster Wallace, the author who took his own life, saying, “Every love story is a ghost story.”

So ghosts haunt “Heart of a Dog” — but so, too, does love.