"The Shaft"
here's the wikipedia.com plot summary:
"Plot summary
When several people die unexpectedly in an
express elevator in a New York City landmark called the Millennium Building, everyone, at first, thinks it's a technical problem. But when repairmen repeatedly can't find any problems with the elevator, it's clear that something else is at work.
A tabloid investigative journalist (Watts) and an elevator mechanic (Marshall) seek to get to the bottom of what's causing the deaths, as officials try to play down the incidents and the government investigates them as terrorist attacks.
The duo eventually discover that the elevators indeed have a life of their own."
That's Naomi Watts and James Marshall!