Prosecutors say 34-year old Darrell Fuller shot and killed Emergency Services Officer Arthur Lopez during a traffic stop in 2012.
He's also accused of killing a Brooklyn construction worker, Raymond Facey, and stealing his car.
The jury deliberated for three hours on Friday before breaking for the weekend.
Police say Fuller had just been in a car crash and was fleeing when Lopez and his partner stopped him near Belmont Park racetrack.
Fuller allegedly shot Lopez in the chest.
Fuller has pleaded not guilty.
In a courtroom packed with relatives of the victims, police officers and officials, prosecutor Mitchell Benson told jurors there is overwhelming evidence that Fuller killed both Lopez and Facey.
"He wanted to get away from the police and he killed Officer Lopez," Benson told jurors as relatives of the 29-year-old officer wiped away tears in the front row of the gallery.
Defense attorney Kenneth St. Bernard insisted that prosecutors had failed to prove their case, arguing that there were no eyewitnesses to either shooting.
But Benson countered that while Lopez's partner, Officer Clarence Hudson only heard the gunshot that killed his partner he had seen Fuller driving the vehicle that they had been pursuing and also saw him flee the shooting. He added that Fuller left his driver's license, wallet and other personal items behind in his car when he shot and killed Facey moments after fleeing the police shooting scene.
"The evidence in this case was abundant, it was overwhelming," Benson said. He apologized to jurors for perhaps giving them too much information. "We wanted to make sure that you had the evidence that you need to come up with the proper verdict."
Lopez and Hudson were patrolling near the Nassau-Queens counties border when they saw a car driven by Fuller collide with a van, authorities said. Fuller allegedly drove away and the officers pursued him as he entered the Cross Island Parkway, headed south.
The officers followed as Fuller left the highway at the next exit, apparently driving with at least one flat tire and the rear bumper dragging along the ground. Fuller was out of his vehicle, Benson said, when Lopez approached him armed with a stun gun. The prosecutor said the officer got within about 5 feet of Fuller before he opened fire.
Lopez died at a nearby hospital. Facey was parked on the side of the parkway making a phone call when prosecutors say Fuller approached and shot him before stealing Facey's car.
Police said Fuller was arrested hours after Lopez and Facey were killed. Fuller first fled to a nearby day care center, where he called a friend to pick him up. That friend later shot Fuller in the arm and leg in an attempt to make it appear that Fuller had been a victim of the carnage, Benson said.
Fuller served four years in prison after pleading guilty to attempted murder in 2005, authorities said. He was jailed again in 2010 after violating his parole on a drug arrest and was released in 2011, prosecutors said.
(The Associated Press contributed to this report.)