The premise of “Fido” is so fantastic you almost forgive the shortcomings of the movie itself. It’s set in an alternate version of the 1950s, when zombies have risen up from the graves, warred with the living, and eventually been subdued into docility. Now every family on the block has a zombie as a household servant or groundskeeper.

We’re treated instantly to a fantastically sunny production design replicating the cheeriness of the ’50s. Everything is just as we remember it from Doris Day movies and “Leave It to Beaver,” with domesticated zombies added to the mix. And we meet young Timmy Robinson (K’Sun Ray), embarrassed because his family is the only one in the neighborhood without a zombie. Timmy’s shame is compounded when the head of security for ZomCon, which manufactures the zombie collars, moves onto his street. They have SEVERAL zombies working at their house!

But Timmy’s dad, Bill (Dylan Baker), doesn’t trust zombies, even with the radio collars that keep them passive. Timmy’s mom, Helen (Carrie-Anne Moss), wants one to help with housework, though, and she eventually persuades her husband to allow one in the house.

Most families don’t bother naming their zombies. Timmy calls theirs Fido. (Fido is played by Scottish comedian Billy Connolly, almost unrecognizable with short hair and pale, gray skin.) Fido has traits of a butler, a maid, and a dog. He does as he’s told, and he protects Timmy from bullies. Soon he’s Timmy’s best friend and confidante.

And then Fido’s collar malfunctions and he does something zombie-like to an old lady. Oh, and he has a crush on Timmy’s mom. Maybe Dad was right about these guys….

Canadian filmmaker Andrew Currie, writing with Robert Chomiak, has envisioned a film that lies somewhere between “Lassie” and “Dawn of the Dead,” intended as a parody more than an actual horror movie. There are horror elements — severed limbs and whatnot — but the idea is to amuse us more than scare us.

It does that (amuse us, I mean) fairly well for a while, but the sad fact is, as great a premise as we have here, it wears thin. Campy humor is difficult to sustain for any length of time because it remains, by definition, on the surface of the characters’ emotions and personalities. The plot becoming needlessly complicated near the end doesn’t do the film any favors either.

“Fido” has many laughs, and its satire of suburbia (and class relations, and the illegal-immigration debate, and so on) is often trenchant. Yet I found myself wanting to laugh more than I actually laughed. I suspect the concept would make a great 30-minute short.

B- (1 hr., 38 min.; PG-13, some violence and blood.)