Richardson suffered a head injury Monday while taking a beginners ski course in Quebec and . A statement from the family did not give details of the precise cause of death.
Yves Coderre, director of operations at the emergency services company that sent the medics to the Mont Tremblant resort, told The Globe and Mail newspaper Wednesday that ski patrollers requested an ambulance after Richardson fell.
The paramedics who responded were told they were not needed, said Coderre, whose company, Ambulances Radisson, serves Mont Tremblant, about 80 miles northwest of Montreal.
"They never saw the patient," Coderre told the Globe and Mail. "So they turned around."
Coderre said another ambulance was called later to Richardson's luxury hotel. By that point, her condition had gotten worse and she was rushed to a hospital.
It wasn't immediately clear who sent the first ambulance away or why, but a resort spokeswoman said Tuesday that Richardson initially said that she was fine.
The resort also issued a statement Tuesday that said Richardson didn't appear hurt and was walking around shortly after the incident.
"She did not show any visible sign of injury but the ski patrol followed strict procedures and brought her back to the bottom of the slope and insisted she should see a doctor," the resort said in its statement.
The ski resort said the instructor and a ski patroller accompanied the actress to her hotel, where they again recommended she should be seen by a doctor.
Coderre said victims of head trauma often believe they are fine, a mistake that can cost them their lives.
"When you have a head trauma you can bleed. It can deteriorate in a few hours or a few days," he told the newspaper.
She was eventually moved to a Montreal hospital before being transferred to New York.
Messages left by The Associated Press with Coderre at Ambulances Radisson and the Mont Tremblant resort were not immediately returned.
Richardson was married to Liam Neeson and was the daughter of Vanessa Redgrave. She and Neeson have two sons.
"The entire family are shocked and devastated by the tragic death of their beloved Natasha," a spokesperson for the family said in a statement Wednesday.
A small, private funeral is planned, CBS News correspondent Bianca Solorzano reported.