A motorist who came upon the scene just north of the Planting Fields Arboretum reported seeing a disturbance -- including aggressive movement -- in the van, a 1999 Toyota Sienna, followed by loud noises, said Det. Lt. John Azzata, commanding officer of the Nassau homicide squad.
"It is my belief that the male was the initial shooter," Azzata said.
Azzata said a handgun was found inside the car.
The man was in the passenger seat and the woman in the driver's seat, police said.
Azzata said police received a call Monday morning about a vehicle stopped on the roadway with two individuals possibly needing assistance.
Later, when officers arrived on the scene, they found the car stopped on the two-lane roadway.
Police said Monday night they will not release the identification of the man and the woman until both autopsies are completed sometime Tuesday.
Police suspect neither lived in the immediate area of Matinecock, but lived elsewhere in Nassau County and may have been "romantically involved."
The woman, who was in her mid-40s, worked in the vicinity of the crime scene and had been on the way to her job, police said.
She had children, detectives said.
Monday was the man's 50th birthday, according to authorities.
Detectives gave no motive for the shooting.
With Tania Lopez