With something as far-fetched as “Don’t Let Go,” it’s only necessary for a premise to sustain itself for as long as the movie lasts.

This one does that … just barely. But don’t try to scrutinize it later.

“Don’t Let Go” is a cop picture with a supernatural curveball. Our hero is LAPD detective Jack Radcliff (David Oyelowo), a hard-working guy with few distinguishing features — in fact, he’s got almost no character at all.

In the first minutes of the movie, Jack discovers an awful crime: his brother, sister-in-law, and beloved niece Ashley (the convincing Storm Reid, from “A Wrinkle in Time”) have been shot to death.

The brother (a too-small role for the great Brian Tyree Henry, from “If Beale Street Could Talk”) was a ne’er-do-well, but Jack had a close relationship with Ashley. Maybe closer than he thought.

The curveball is that Ashley keeps calling him, from two weeks before the murders. She’s in some kind of time-slip, although she doesn’t know it. Can Jack find a way to communicate with her and stave off the coming disaster?

The writer-director, Jacob Aaron Estes, goes all in on the idea. And at times he captures something haunting in the mysterious connection, especially in the scenes where Jack and Ashley are occupying the same space — their favorite diner booth, for instance — two weeks and an eternity apart.

That kind of thing brings some legitimate shivers. The gimmick is a bit like the central idea of “Frequency,” a 2000 thriller with Jim Caviezel talking to his long-deceased dad Dennis Quaid over a shortwave radio. But with more dropped calls.

Estes has made two previous films, “Mean Creek” and “The Details,” and both were unusual. Maybe he’ll make a really distinctive movie someday, but “Don’t Let Go” is too dependent on its storytelling trick to truly take off.

Plus, there’s a re-start that happens at one point that I still don’t understand. And with this kind of premise, I shouldn’t have to try to understand it after the movie’s over (see above rule).

“Selma” star Oyelowo provides a sturdy center, even if his talent isn’t exactly stretched. Alfred Molina is Jack’s blustering boss, and Mykelti Williamson his fellow cop (with no time-bending explanation of why he looks the same as he did in “Forrest Gump” 25 years ago).

Ethan Gold’s music is quirky enough to make an impression. No doubt about it, “Don’t Let Go” tries to be something different — but its cop-movie cliches and shock effects keep dragging it back into standard time.

“Don’t Let Go” (2½ stars)

An LAPD detective (David Oyelowo) begins getting calls from his niece — two weeks after she and her family were violently killed. This supernatural premise just barely sustains itself for the film’s running time, and the idea never quite takes off to the next level. With Storm Reid.

Rating: R, for violence, language

Opening Friday: Alderwood Mall, Everett Stadium, Meridian