Investigators believe that the veteran NYPD cop shot during a chaotic confrontation with a gun-toting teen Sunday was struck by friendly fire, law-enforcement sources told The Post.

Detective Robert Karroll was hit in the back by a slug — and only saved from potentially deadly injuries by his bulletproof vest — around 4:15 a.m. when a deranged 18-year-old ran up on an unmarked police car in Crown Heights, authorities have said.

Investigators believe that the veteran NYPD cop wounded during a chaotic confrontation with a gun-toting teen Sunday was struck by friendly fire. Obtained by NY Post An NYPD officer holds up a photograph of the firearm allegedly used in a shooting in Brooklyn on Sunday. Luiz C. Ribeiro for NY Post

Karroll — a married dad of three who was just 10 days from retirement — was in the vehicle along with three other officers, all of whom were in uniform, officials have said.

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When the suspect flashed his gun in front of the officers, three of the four cops fired — missing the suspect but apparently hitting Karroll, sources said, citing a preliminary probe.

The bizarre set of events began to unfold around 4:05 a.m., when surveillance video captured the seemingly hyped-up armed teen chatting with four people outside a Nostrand Avenue deli.

The teen whipped out an SAR 9 mm handgun, and over the next 10 minutes, pointed it wildly at one of the men outside the deli, walked inside the store, came back out and shot at a passing Uber — his apparent target, according to sources. Neither the Uber driver nor their passenger is hit, sources said.

The teen then walked behind the cops’ unmarked SUV with his weapon visible, sources said.

Detective Robert Karroll was hit in the back by a slug around 4:15 a.m. when a deranged 18-year-old ran up on an unmarked police car in Crown Heights Luiz C. Ribeiro for NY Post

He proceeded to go along the driver’s side, then in front of the SUV with his gun in his hand — prompting the cops to fire, sources said.

The suspect was not hit, but Karroll was struck in the back — saved by his police vest.

The cop car was riddled with bullets during the chaos.

A female cop also suffered minor injuries.

The unidentified gunman fled but was nabbed several blocks away, at Union Street and Rogers Avenue, after resisiting arrest and having to be tased, officials said..

He is awaiting charges, sources said.

Karroll was released from the hospital hours later and  is expected to make a full recovery, police said.

The teen has no prior arrests in the Big Apple, but has at least one shoplifting charge in Essex County, NJ.