The mystery has deepened over the death of glamorous bikini designer Martha Nolan-O'Slatarra who died on board a Hamptons yacht with an insurance tycoon last week.

The grief-stricken family of the 33-year-old, who have now travelled from Ireland to the U.S. to bring her body home, have demanded a second post-mortem amid claims she died of a suspected drug overdose.

Sources say the swimwear brand founder headed to the luxury Montauk Yacht Club on the evening of August 4 to have a meeting with insurance mogul Christopher Durnan, 60.

Durnan - a guitar-playing widower linked to several boats named after Grateful Dead songs - is believed to have invested more than $200,000 in the Irish beauty's bikini boutique.

But the night ended in horror when the American business man dashed down the dock naked around midnight screaming for help and indicating that Martha had passed out.