Police are exploring this theory because one of the Richardson family's four bodyboards is missing, said Det. Sgt. Robert Gurney, lead investigator.
"The family was on the water all weekend," Gurney said, "and the idea that he went missing from the beach or the ocean is absolutely a possibility . . . The missing board supports that."
Police on Monday released a photograph of a bodyboard -- red with a star pattern -- similar to the one that is missing.
Gurney said that maybe a beachgoer or someone walking the beach picked up the missing board. If so, the exact location where it was found could help in their search, he said.
"We have found other boards," Gurney said of the police search, "but not one that matches the photo."
Richardson was last seen by one of his sons about 1 a.m. in the family's motel room, Gurney said. Every indication is that he went back to sleep "and when the family woke up later that morning he was not in the room."
Richardson, vice president of development -- a fundraising post -- at Huntington Hospital, had been taking early-morning walks on the beach during his vacation. His family thinks he went out about 6 a.m. the day he disappeared and never returned, according to police.
The family did not respond to a request for comment.
Richardson held top fundraising and alumni-relations positions at the Diocese of Rockville Centre's Mercy Medical Center, Hofstra University and St. John's University School of Law before joining Huntington Hospital.
In July, he was appointed to the board of the Huntington Chamber of Commerce.
Anyone with information on the case is asked to call the East Hampton Town police detective division at 631-537-7575. All calls will be kept confidential.