An NYPD lieutenant’s 13-year-old son threatened to kill another boy, then gashed his head with a metal object but was let go and not charged, the victim’s parents allege.

The boy was attacked in Brooklyn’s Carroll Park on June 7 after the cop’s son sent the injured kid a photo of himself holding a bullet between his teeth with the message “It’s me.”

The teen posted a second photo of six Gold Dot hollow-point bullets — the ammo the NYPD uses — writing to the 12-year-old: “U r f–king dead,” according to his Instagram direct messages reviewed by The Post.

He added: “just lookin for my gun I found my bullets.”

The chilling threats outraged the target’s parents.

“You can’t cyberbully other kids and threaten to kill them without any consequences,” mom Natalie Nevares told The Post. “This is a public safety concern.”

Her son’s head wound needed three staples to close, but when Nevares followed up with cops from the 76th Precinct, she was told the alleged attacker had been released and no further action could be taken.

An officer called her while her son was being treated and asked, “What do you want to do?” she says. “It sounds like a scuffle between two boys. You don’t want to ruin this kid’s life.”

An NYPD report indicates that the assault case against the 13-year-old, whose dad is NYPD Housing Lt. Kevin Walsh and lives near the 76th Precinct station house, was closed.

A cop at the precinct e-mailed Nevares, “It is already finished on our end. Since it involves minors, there is no ‘pressing charges.’ ”

A day after the incident, a friend of the accused teen put up photos on Instagram celebrating his release. The pal wrote “get outta jail free card.” Another wrote, “When your dad has one.”

The report does not indicate there were any witnesses to the attack, but Nevares found a video of the assault on Instagram that shows a group of boys watching as Walsh’s son strikes her son, knocking him to the ground.

The injured boy then gets up and shoves Walsh’s son.

The footage, which she e-mailed to police, shows a “concealed metal object in [the attacker’s] right hand. . . which is passed to his left hand afterwards,” she claims.

She also sent photos of her son with blood dripping down his neck before an ambulance arrived.

Lt. Walsh identified himself when reached by phone but when asked about the incident involving his son, he said, “I have no idea what you’re talking about,” and hung up.

Police typically refer serious charges against juveniles to Family Court for fact-finding.

If a judge finds a crime was committed, the offender may be ordered to undergo a mental-health evaluation and sentenced to a juvenile detention facility or released on parole.

The NYPD would not answer questions about the case, saying only, “The matter is under internal review.”

Click Here: titleist golf balls

The two boys attend different schools, and Natalie and husband Lane have been trying to arrange a meeting involving both families and school officials.

“We have no interest. There’s nothing more to discuss,” the mother of the 13-year-old told The Post.

The Nevareses say they want to pursue the matter with authorities. “We want to hold our son’s assailant accountable for his actions,” Lane said.