PC Gareth Browning was on foot in Whitley, Reading, in November 2013 when he was hit by a black Mazda driven by Luke Hayward.
Hayward was jailed for nine years in 2014 for causing grievous bodily harm with intent and dangerous driving.
PC Browning, who was medically retired, died on Saturday aged 36.
Thames Valley Police said following PC Browning's death it would liaise with the coroner and Crown Prosecution Service.
Chief Constable Francis Habgood described his former officer as "hugely respected".
He said he had needed "constant care" following the crash.
"Our thoughts are with Gareth's family, friends and colleagues at this difficult time," he added.
"We continue to support Gareth's family as well as staff and officers who have been affected."
An officer who was hit by a stolen car as he tried to stop it getting away has died from his injuries more than three years later, police said.