A Long Island student who turned down an alcoholic toast at her sister’s 21st-birthday party because she was the designated driver died Monday from injuries she suffered in a car crash with a drunken off-duty NYPD police officer, relatives and officials said.

Vanessa Raghubar, 22, was out with family Sunday celebrating her sister, Maria, 21, turning old enough to legally drink, the sisters’ cousin told The Post.

“We went for dinner, and then we went to a bar,” said the relative, Diana Chand, by phone from Jamaica Hospital, where Maria Raghubar had just undergone surgery for her injuries, which include a broken pelvis and severe internal damage.

“Vanessa didn’t drink,’’ Chand said. “She refused because she was driving some of us back. They did blood tests at the hospital after she was hit — it showed she didn’t have a drop.”

Vanessa was driving a Honda with Maria and her boyfriend in the back seat when the car was rear-ended by a Mercedes driven by Officer Neville Smith, 32, authorities said.

The crash occurred at 4 a.m. Sunday on the Van Wyck Expressway in South Ozone Park.

Maria’s boyfriend was treated and released. Smith suffered minor injuries.

Smith, 32, who works in the 48th Precinct in the Bronx, was charged with driving while intoxicated, vehicular assault, assault, and refusal to take a breath test.