In theory, putting “possession” in the title of a horror movie should add to its box-office allure. But it probably won’t take long for word to trickle out that “The Possession of Hannah Grace,” after the first five minutes, is not an exorcism movie. Rather, it’s about the corpse of a girl who dies during an exorcism, so technically speaking you could say that it qualifies. But viewers hooked on the spectacle of demonic possession tend to like their satanic tropes served neat. “The Possession of Hannah Grace” serves them sloppy, if not without a certain random soupçon of grisly style.

Just about the entire film is set in a morgue. And though it stars Shay Mitchell, from “Pretty Little Liars,” it has her playing a character with almost no personality: Megan, an ex-cop and (barely) recovering alcoholic who lands a job working the graveyard shift as a...