The accident happened at 4 a.m. Sunday on the Van Wyck Expressway southbound at Rockaway Boulevard in South Ozone Park.
Investigators say 32-year-old Neville Smith, who was off-duty at the time, slammed into the rear of a Honda.
Two women, identified as 22-year-old Vanessa Raghubar and 21-year-old Maria Raghubar, were rushed to Jamaica Hospital.
Authorities say Vanessa Raghubar died from her injuries early Monday.
"She's was the most beautiful, loving, caring, understanding person I ever had in my life," aunt Esther Mongul said.
The sisters, described as closer than twins, were heading home from celebrating Maria's birthday.
"My daughter was such a sweet child," mom Janice Perry said tearfully. "My daughter was so educated. She had a big future ahead of her. And that someone would just take her life is wrong. The cop was wrong."
Maria Raghubar remains in critical condition and has reportedly spent much of Monday in surgery, as doctors desperately try to save her life.
"We have to keep our hopes high and pray to God that she survives it," Perry said. "We just don't know."
Maria's boyfriend Justin Harricharra, who was in the back seat, suffered brain, back and spinal injuries.
"It really foggy," he said. "What I remember was waking up in the hospital, and them telling me I was in an accident."
Maria Raghubar's injuries were described as extensive.
"She had so many complications," Mongul said. "Broken pelvis, a smashed bladder, damaged intestine."
Vanessa Raghubar was a York College student studying psychology and set to graduate in June. She was also a talented artist. Now, her family is preparing for her funeral while standing by Maria's bedside and vowing to see the person responsible for their heartbreak held accountable.
"We need justice for our baby," Perry said. "She can't...it can't go like this. We need justice."
Smith, who works out of the Detectives Bronx Bureau, also remains in the hospital in stable condition.
He is charged with vehicular assault, assault, DWI and refusal to take a breath test.