The 33-year-old fashion designer from Carlow was found unresponsive on a boat owned by millionaire Christopher Durnan at Montauk Yacht Club in August 2025.
He sought help, but she subsequently died at the scene.
Police investigating her death have stated that the post-mortem examination results are inconclusive but show "no evidence of violence" in her death.
In August, the administrators of Martha's estate launched proceedings against Durnan, but it has taken a two-month search to track him down.
They allege that he "intentionally and wrongly" assaulted Martha and that "gross negligence" and "reckless and wanton conduct" contributed both to her injury and death.
Her family filed a "summons with notice" in New York County on 4 August asking for damages for "wrongful death" and damages for the "personal injuries and conscious pain and suffering" she sustained before her passing.
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Private investigators personally served Durnan with a summons notice on 1 October, the Irish Independent reports.
Filings show that a number of unsuccessful attempts were made to serve him over the past two months. That included attempts to serve him at three addresses identified by his lawyer in New York.
An attempt to get his lawyers to accept service was also unsuccessful.
He was eventually served on 1 October at a property on Hollywood Street in Florida after being followed to the address by a process server and private investigator.
It's claimed that after confirming his identity, Durnan remarked that he "was surprised it took you so long."
He was given 20 days from the date of service to respond to the summons.
* This article was originally published on Evoke.ie.