Neeson's 31-year-old nephew Ronan Sexton fell on Sunday, and now apparently is in critical condition, reported Ace Showbiz.
A spokesperson for Sussex police confirmed the incident, adding that they did not treat it as suspicious.
Neeson, 62, has been in contact with his sister Bernadette Sexton as she stays with her son at the hospital.
"Bernadette is not in at the moment because she has been at the hospital all day in Haywards Heath visiting Ronan. I do not want to comment further," her partner Harry Shannon said at a family home in Worthing, West Sussex.
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