It's the scenario from hell. A rookie cop is on patrol in the Louis H. Pink Houses in East New York, where the NYPD is trying to stop a crime uptick. He enters a dark stairwell with his partner -- carrying a flashlight in one hand and his service pistol in the other.

Simultaneously, one flight down, a young couple opens a door to the same inky black staircase because -- as usual -- the elevator is taking forever to arrive.

As they enter the stairwell, the cop's weapon fires -- and Akai Gurley, 28, the father of a 2-year-old girl, is fatally hit.

It's a ghastly tragedy by any measure. Gurley was a "total innocent," said NYPD Commissioner Bill Bratton, who called the shooting an "unfortunate accident."

Yet coming as it does amid tensions over the death of Michael Brown, 18, at the hands of a Ferguson, Missouri, police officer and the death of Eric Garner on Staten Island last summer at the hands of the NYPD, Gurley's death is yet another outrage on a pile of grievances.

So the mission of Mayor Bill de Blasio and Bratton now is to restore the battered trust and credibility of crucial local agencies like the NYPD and New York City Housing Authority, which supervises the Pink Houses.

If they don't, the anger will only grow.

They have a litany of questions to answer:

Why was the stairwell dark in the first place in the tower where Gurley was shot? Pink Houses has seen long-standing problems with crime, and dark stairwells are crime magnets. De Blasio campaigned last year with a vow to fix the housing authority's problems. And yet nobody can keep staircase lights and elevators working properly?

Why were two rookies working the Pink Houses stairs in tandem, as news reports have it? Bratton made a point in 2013 of criticizing his predecessor, Ray Kelly, for using rookies together to handle stop-and-frisk operations. Would probationary Officer Peter Liang have drawn his weapon in the presence of a seasoned supervisor? And why did he fire? Was it an accident? Panic?

New Yorkers deserve a full account -- and not just from the NYPD.

This is a public outrage on many levels.