Cops like NYPD suicide victim Robert Echeverria keep their mental health struggles a secret for fear their bosses will take their guns away — and demote them to a desk job where they’ll lose their overtime pay, his sister told The Post.

“I offered my brother $500 to go to a private psychiatrist,” Eileen Echeverria said Friday, two days after the troubled officer killed himself in his Laurelton, Queens home.

“He said, ‘I can’t go to a psychiatrist because they’ll put me on the rubber gun squad,” she said. “They’re going to find out,” she said he told her. “Forget it. I’ll be all right.”

Before Echeverria, 56, held a gun to his head and pulled the trigger on Wednesday, she had repeatedly warned the NYPD’s Internal Affairs Bureau that he was a risk to himself or others, the sister said, speaking from her home in West Islip, NY.

Unless the NYPD gets more pro-active about cop suicides, the tragedies will continue to happen, she said. She urged that the NYPD reach out to at-risk officers first — rather than wait for cops to ask for help they may never seek.

In the days since her brother’s suicide, Echeverria has been an outspoken critic against the mayor and the NYPD.

On Thursday, she revealed that she had warned the NYPD as recently as June that her brother was a danger to himself and others so long as he kept his gun.

The NYPD “raided” the home he shared with his wife and 11-year-old daughter, confiscated his weapon and had him speak to a doctor, she said. But within days he was deemed alright had his gun back.

“Mayor De Blasio puts a phone number on the TV and says for cops to reach out,” she complained on Friday.

“Now their latest thing is to have an app on the phone. They’re never going to do it,” Echeverria told The Post.

“Because if they do, they know their job is in jeopardy. They’re not going to get overtime. They’re going to be put on the rubber gun squad, as they call it. They’re never going to do that.”

Her brother had struggled since childhood with mental illness, she said, and by the time he killed himself was struggling not to lose his heavily-indebted Queens house.

He’d also become a hoarder, his house so cluttered that one could barely walk in it, she said. An attached rental unit was “filled” with his pet ferrets, she said.

“When they raided it” in June to briefly take his guns, “they didn’t see that as a sign of mental illness? … I’m not talking about someone being sloppy,” she said. “I’m talking about you can’t get in the door.”

Echeverria said her “dream” is for NYPD to employ a large staff of counselors who can reach out to cops — before tragedy strikes — rather than wait for cops to come to them.

“Why can’t the city of New York hire a bunch of counselors and randomly call in officers and say, ‘You know what, yesterday, Officer Jones, you were spat at. How you dealing with that? Officer Smith, there was a bucket thrown.'”

She added, “I know it’s expensive, but it’s a dream I have.

“Internally the NYPD is broken. We know of nine suicides a year. I keep getting reached out to so many people” whose lives have also been touched by an officer’s suicide, “five years ago, four years ago, but they didn’t talk about it.

Should another mother ever have to go through that? Should a wife? Should children?”