Newark officer Louis Santiago, 25, then returned to the scene of the accident with the dead man strapped into the back seat and alerted authorities, prosecutors say.
The officer allegedly hit 29-year-old nurse Damian Dymka as he walked on the hard shoulder of the Garden State Parkway in the early hours of 1 November.
Investigators say that neither Officer Santiago, or his passenger, Albert Guzman, called 911 or gave aid to Mr Dymka after he was struck.
The men are accused of returning to the scene of the accident multiple times before putting Dymka in the Honda Accord and driving back home where Mr Santiago discussed what to do with his mother, Annette Santiago, and Mr Guzman.
Officer Santiago then returned to the scene with his father, who is a Newark police lieutenant, and called 911.
Officials say that when New Jersey State Police arrived they found Mr Dymka dead in the back seat.
Louis Santiago was charged with reckless vehicular homicide, desecrating human remains, tampering with physical evidence and other charges that include official misconduct.
Mr Guzman, 25, and Ms Santiago, 53, are charged with counts that include conspiracy to desecrate human remains and hindering apprehension, according to the Essex County prosecutor’s office.
All three were arrested and released with conditions.