John Everhart of Bethesda, Md., was driving the SUV when police say it overturned on Interstate 80 in Paterson on Sunday.
The 20-year-old had adopted a 40-pound basset hound mix named Bodhi about a year ago.
His stepmother called Paterson Chief Animal Control Officer John De Cando on Tuesday to say the passenger who survived the crash said the dog had run away.
De Cando says Bodhi is the only thing Liz Everhart has left of her stepson.
The family has used a Petfinder.com service to send fliers to veterinarians and animal shelters in the area.
Anyone with information about the dog's whereabouts should contact the Paterson Animal Shelter at 973-881-3640.