Police say Ronan Sexton, 31, was out with friends when he fell about 20 feet from a phone booth beside the pier in the southern England seaside resort of Brighton.
"Just after 4 a.m, on Sunday June 22, a 31-year old Worthing man had climbed on to the top of a telephone kiosk outside Brighton Pier when he fell some 20 feet to the ground, sustaining a serious head injury," said a police spokesman.
"He was taken to the Royal Sussex County Hospital and was later transferred to Hurstwood Park Hospital in Haywards Heath where he is currently in a critical condition.
"The man had been enjoying a night out with friends, who were present when he fell, and the incident is not being treated as suspicious. There is no further police investigation."
Sussex Police said Friday there were no suspicious circumstances to the incident.
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Sexton's mother, Bernadette, is the sister of the Irish actor.
"Ronan is receiving wonderful treatment from the dedicated staff at Hurstwood Park," said his family in a statement. "We gratefully receive all the love, support, prayers and good wishes for Ronan's full recovery to good health. We would appreciate privacy at this time."
Neeson's wife, actress Natasha Richardson, died in March 2009 after hitting her head while skiing.
"It was never real. It still kind of isn't. There's periods now in our New York residence when I hear the door opening - she would always drop the keys on the table and say hello," said the Taken actor. "So any time I hear that door opening I still think I'm going to hear her. Grief hits you like a wave, you get this profound feeling of instability."
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