Troubling video shows a city employee dispatched to Chinatown in the wake of deadly attacks on four sleeping vagrants handing out mental health pamphlets to random people on Tuesday — while completely ignoring a homeless man napping on a nearby bench.

The worker and two others from the Department of Health and Mental Hygiene spent about 15 minutes in the Kimlau Square park following Mayor Bill de Blasio’s Monday promise to flood the area with homeless outreach workers in response to the grisly bludgeonings early Saturday.

In a video clip shot by The Post, the worker — who wore a royal blue windbreaker with an “NYC” logo on the front and “DOHMH” in large white letters on the back — says, “We are here to respond to the situation that happened here.”

But he declined to say why he and his colleagues didn’t show up until shortly before 2 p.m., saying he’s not allowed to talk to the news media.

At one point, the worker tried to hand a pamphlet promoting the city’s “NYC WELL” crisis-counseling program to a Post photographer.

The pamphlet — part of first lady Chirlane McCray’s controversial, $1 billion “ThriveNYC” initiative — contains messages in English, Spanish and 12 other languages, including Bangla and Urdu.

When the worker neglected to approach a vagrant lying on a park bench, a reporter asked, “Sir, I couldn’t help but notice that you didn’t actually speak to any of the homeless people out here, just the other citizens. Are you going to try to do that?”

“Like this gentleman here — are you going to try to wake him and speak with him?” the reporter added.

The worker said that he didn’t want to “disturb” the homeless man and instead tried in vain to give pamphlets to several passersby before finally going over to the bench.

The vagrant opened his eyes and took a pamphlet when the worker walked up, tucking it by his side on the bench.

The Post also spotted one of the DOHMH workers goofing off and snapping photographs of a musician playing “Auld Lang Syne” on a saxophone, then summoning her colleagues to look at the shots.

Additional reporting by Julia Marsh