New Jersey state trooper Michael Patterson was on patrol recently when he pulled over a white BMW for a routine traffic stop.

He asked the driver for his license and registration, and the two started making small talk. It turned out that the driver, Matthew Bailly, is a retired police officer from Piscataway, a township in central Jersey.

Patterson grew up in Piscataway, and they soon realized they knew some officers in common. That’s when the chitchat took a remarkable turn.

“What street did you live on?” Bailly asked Patterson, 26.

“Poe Place,” Patterson replied.

Bailly always remembered Poe Place, he told Patterson, because he helped deliver a baby in a house there as a rookie. You don’t forget something like that, even almost 27 years later. Bailly said he even remembered the baby’s name, Michael.

Patterson’s mind raced — he was born at his parents’ house on Poe Place. Patterson had heard the story countless times from his mother: His dad called 911 in a panic. A police officer showed up to help.

Patterson put the pieces together and blurted out: “That was me.”

“Get the hell out of here,” Bailly said in disbelief. In the blue house? The colonial?

“That was me. That was me,” Patterson repeated with a huge smile, extending his hand inside the car. “Thank you for delivering me.”

Bailly at first thought Patterson was pulling his leg. Surely, it would be too much of a coincidence for this trooper to be the kid he helped deliver almost three decades ago.

Then he saw the sincere look on Patterson’s face.

The men laughed. They shook hands. They were in shock.

Patterson did not give Bailly a ticket for having a cover over his license plate, the original reason he stopped him that morning on June 1.

Patterson’s body camera showed the whole interaction lasted eight minutes, he said.

When the men drove away, they each called their wives, and the wives asked if they had taken a picture. They hadn’t. They hadn’t even exchanged information.

But Patterson knew Bailly’s address from the traffic stop, so he went by and left him a note. Bailly responded right away and invited him over. Patterson brought his mother.

Then things got a little emotional.

“There were a couple of tears shed perhaps by my wife and his mom,” Bailly said.

Patterson’s mother, Karen Patterson, told the story she tells every year on Michael’s birthday, Oct. 5.

It was 1991, and she was due any day. She decided to go to the grocery store with her oldest son, Terek, who was 10. She began having contractions so severe that she was bent over in pain as she checked out.

Her water broke before she left the parking lot. She drove home with her legs clamped tight.

When she arrived home, her husband, Bobby Patterson, ran outside and carried her in. He called 911 and her doctor.

Bailly, new on the force, arrived at the house soon after. Within minutes, the baby was born. The umbilical cord was wrapped around his neck, and Bobby Patterson had to gently lift it off. They named the baby Michael.

Bailly, who helped make sure everything was okay at the house and got mother and baby into an ambulance, didn’t have kids yet — it was the first time he’d seen a baby be born. It was monumental for him, and he, too, has told the story countless times over his career.

When the families met last week at Bailly’s house, no one forgot to take photos.

Patterson and Bailly got together for pizza another time. They say they will remain friends, for sure. They joke that Bailly might help deliver Patterson’s baby — his wife, Alison, is due in a few weeks.