A relative said that Genesis Rincon's organs were donated. She was declared brain-dead after she was shot Saturday night.
Police do not believe the 12-year-old was targeted by the shooter. She was riding a scooter on Rosa Parks Boulevard at the time.
Rincon's family gathered at St. Joseph's Hospital in Paterson to say farewell. A weeping aunt recalled that Genesis always "hugged and kissed" her when they saw each other.
"I don't think poor kids deserve to die like this," a cousin, Wendy Rodriguez, told WNBC-TV.
A vigil was held Monday and another is planned for Tuesday. Rev. Della Fischer, a spokesman for the family, called for more police on the street in Paterson on Monday.
"Paterson, we're in trouble, and we're not going to be quiet no more -- we're going to make noise," she said.