An NYPD cop killed himself behind a Staten Island precinct on Friday — the third member of the department to commit suicide this month, sources told The Post.

Officer Mike Caddy, 29, was found inside a vehicle on Wilcox Street behind the 121st Precinct with a self-inflicted gunshot wound just before 4 p.m., the sources said. He was pronounced dead at the scene.

Sources described Caddy as a domestic-violence officer with seven years on the job. He was in uniform and working when he took his life.

The cop’s death comes just one week after NYPD officials urged department members to speak up and seek treatment for mental-health issues — following the suicides of two veteran officers.

“In less than 10 days’ time, the NYPD has lost three of its own to suicide: a respected chief, an experienced detective, and — today about 3:50 p.m. outside the Staten Island precinct at which he worked — a promising, 29-year-old police officer,” said NYPD Commissioner James O’Neill in a statement. “This is a mental-health crisis. And we — the NYPD and the law enforcement profession as a whole — absolutely must take action. This cannot be allowed to continue.”

Homicide Detective Joe Calabrese, 58, was found dead on June 6 of an apparent self-inflicted gunshot wound at Brooklyn’s Plumb Beach.

Steven Silks, the deputy chief of Patrol Borough Queens North, took his own life in a similar manner a day earlier. Silks, 62, was found just blocks away from his office at the 112th Precinct station house in Forest Hills.

Following those suicides, Chief of Department Terence Monahan said in a video posted to his Twitter account: “We’ve lost two of our members of service due to suicide and this is something we have to talk about. This isn’t something that we can just keep in whispered tones and not have the conversation…This has to be open. We need everyone in this agency to be willing to talk about this.”

The NYPD offers services with the Employee Assistance Unit and the Chaplains Unit and also encourages the use of Police Officers Providing Peer Assistance (POPPA), which is external from the department. But a high-ranking police source pointed out that it remains relatively easy for ­officers to commit suicide.

“We have the means — an easy way to do it,” the source said.

The recent spate of suicides has left officers shaken.

“I want every member of the NYPD to know: your city is here for you,” said Mayor de Blasio in a statement Friday. “You are not alone. Help is here. Reach out. We are working with the Police Department to continue to put resources front and center, and that our officers have every possible support.”

O’Neill added, “Cops spend so much of their days assisting others. But before we can help the people we serve, it is imperative that we first help ourselves. There is no shame in seeking assistance from the many resources available, both inside and outside the department. Accepting help is never a sign of weakness — in fact, it’s a sign of great strength. Please, connect yourself or your friends and colleagues to the assistance that is so close by. We must take care of each other. We must address this issue — now — because it will not go away on its own. We must speak out. And we must end this crisis, together.”

Additional reporting by Chris Perez