The Garner and Gurley cases turned on whether the officers either disregarded or failed to perceive an unjustifiable risk of death from their actions, one that a normal person — or in their case, another officer — should have been aware of. In both, the officers deviated from police rules in their encounters, fueling the argument that they should have known the risks that their actions posed.

Such recklessness, legal experts say, would be enough for a second-degree manslaughter charge, the most serious of the six counts against Officer Liang.

In the Garner case, grand jurors had to decide if the force used by Officer Daniel Pantaleo was legally justified in his struggle to arrest Mr. Garner, who weighed more than 350 pounds and was accused of selling loose cigarettes.

Officer Pantaleo wrapped his arm around Mr. Garner’s neck to bring him to the ground, and other officers swarmed in to assist; Mr. Garner later died of a chokehold and chest compression, the city medical examiner found.

The Staten Island district attorney, Daniel M. Donovan Jr., a Republican, followed the standard playbook for politically sensitive killings at the hands of officers. He impanelled a special grand jury and presented testimony from 50 witnesses over nine weeks, including the accused police officer.

Officer Pantaleo narrated videos of the confrontation, telling the grand jury that he was trying to arrest and subdue Mr. Garner with a wrestling move, not hurt him. In contrast, Mr. Thompson presented 14 witnesses — including the officer’s partner and the victim’s female companion — over several days to a regular grand jury that heard other cases.

Officer Liang’s decision not to testify left prosecutors and the jurors facing one key question: Did he consciously disregard the obvious risk that someone might die when he put his finger on the trigger and pointed his gun down the stairway, something he had been trained not to do?