Richardson, 45, part of the Redgrave dynasty of British actors and the wife of Liam Neeson, was flown from Montreal to New York on Tuesday after the accident, a person close to the family, who asked not to be identified because of the sensitivity of the matter, told The Associated Press on Tuesday.
Richardson's condition was very serious and her family was highly distressed, The New York Times reported Wednesday, citing two people close to her family who spoke on the condition of anonymity because they were not authorized to speak to reporters.
The family was to issue a statement late Wednesday morning, CBS News correspondent Bianca Solorzano reports.
Later that evening, a somber looking Vanessa Redgrave, Richardson's mother, was seen in photographs walking into Lenox Hill Hospital in New York City. It couldn't be immediately determined whether Richardson was a patient at the hospital.
Richardson is the elder daughter of Oscar-winning Redgrave and the late director Tony Richardson. She fell Tuesday during a private lesson Monday at the famed Mont Tremblant ski resort.
"We know that she has had an accident but we really do not know any more details," said Kika Markham, who is married to Richardson's uncle, Corin Redgrave. "We are very concerned."
"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," said the statement from the resort, about 80 miles northwest of Montreal.
The ski resort said the instructor and a member of the ski patrol accompanied Richardson to her hotel, where they again recommended she be seen by a doctor. Mont Tremblant spokeswoman Catherine Lacasse said Richardson said she seemed fine at first.
"An hour later she said she didn't feel well. She had a headache, so we sent her to the hospital," Lacasse said. "There were no signs of impact and no blood, nothing."
"It really looks as if she's had a significant head injury, and it really highlights the importance of being evaluated after you have a head injury," Dr. Carolyn Brockington, a neurologist at St. Luke's-Roosevelt Hospital in New York, said on The Early Show Wednesday, based on what she'd read of Richardson's injury.
How can it be that Richardson apparently felt no initial ill effects from here fall?
"With some head injuries," Brockington explained to substitute co-anchor Chris Wragge, "the bleeding that happens in the brain happens slowly, over time. And as the bleeding increases, it starts to push on the brain, and creates symptoms. There is certainly a lag time between the time of the head injury, many times, and (when) you develop symptoms."
And, she continued, it's "difficult" to know when danger lurks. "If you feel fine at the time," she said, "you wonder whether you should really go to the hospital. But when you start to develop certain symptoms, that's the time to really pursue treatment rapidly.
" ... With a head injury, if you develop loss of consciousness or a change of mental status, where you appear confused; if there's a time when you develop weakness on one side or numbness on one side, problems with speech or with the development of a severe headache -- all of those things are very crucial in terms of knowing something's happening with the brain, and it needs to be evaluated quickly."
Richardson's films include "Gothic," "A Month in the Country," "Nell" (in which she appeared with her future husband), "The Parent Trap" and "Maid in Manhattan."
Trained at London's Central School of Speech and Drama, Richardson has had extensive stage experience in the West End and Broadway. She won a Tony in 1998 for playing Sally Bowles in a revival of "Cabaret."
Her maternal grandparents were the actors Michael Redgrave and Rachel Kempson, and her uncle Corin and aunt Lynn Redgrave are both actors. Sister Joely Richardson is also an actress, best known for starring in the TV series "Nip/Tuck."
In January, Richardson and her mother played the roles of mother and daughter in a one-night benefit concert version of "A Little Night Music," the Stephen Sondheim-Hugh Wheeler musical, at Studio 54 in New York.
She married Neeson in 1994, and the couple have two sons, aged 13 and 12.