The family of an Australian model found dead on a superyacht in Greece are demanding answers amid mounting mystery over her death.

A week after Sinead McNamara’s comatose body was discovered on the luxury vessel, relatives said they expected Greek authorities to illuminate them on the “causes and circumstances” of the 20-year-old’s “sudden and unexpected death.”

An inquiry needed to be conducted to reveal the whole truth, their lawyer said.

“Her parents state that Sinead was not facing any problems, was communicating very often with her family and was happy,” the attorney, Charalampos Triantafyllopoulos, said in a statement.

“[They] believe it crucial that the case is thoroughly investigated to shed light on the conditions of her death, as well as the events and incidents that preceded [it], so that the whole truth can be revealed and they can learn what actually happened.”

McNamara was days away from ending a four-month stint working as a staff member on the Mayan Queen IV, owned by the Mexican mining billionaire Alberto Bailleres.

Her mother and sister were en route to Greece to meet her on holiday when the Instagram model was found unconscious and entangled in ropes at the back of the vessel, which was anchored in Argostoli off the Ionian island of Kefalonia.

Desperate attempts were made to revive her before she was eventually airlifted to a private clinic in Athens. With Bailleres already back in Mexico, only crew were on board at the time.

McNamara was excited about her family’s imminent arrival but it has emerged that in her final hours she had also made a tearful telephone call to her mother and brother, Jake, relating an incident involving another crew member aboard the vessel.

The revelation, also contained in the lawyer’s statement, followed reports of the model being embroiled in a relationship break-up.

Greek police initially suggested there was enough evidence to point to suicide but speaking to the Guardian after conducting an autopsy on McNamara, the chief coroner Elias Boyiokas said he had been left with “doubts and questions”.

“The answer lies with the toxicological and histological tests,” said Boyiokas, who heads the coroner’s office in Pireaus. “There was no evidence of ill-treatment … my verdict is death by hanging but there were signs that she may have tried to stop it.”

The forthcoming test results would reveal if the model had a high level of alcohol “or any other substance” in her system, which, he said, she might have been unwittingly given.

While there was no visible proof of violence, the forensic scientist revealed he had also taken skin samples from under McNamara’s nails. “If she was drunk or had been given some pill the question, then, is how did she have the strength to physically hang herself … instead of answers I have been left with more doubts and questions.”

Triantafyllopoulos said authorities also needed to explain why it had taken so long to transfer the model from the six-storey superyacht to the Greek capital.

“In addition, the family has requested to find out the reasons for the long delay between the time of the unfortunate incident and Sinead’s transfer to an Athens hospital,” his statement said. “She had been unconscious for several hours in a comatose condition and every minute was critical to her life.”

Prior to her death, witnesses on the Greek island described how the young Australian had been in high spirits, enjoying a night out with fellow crew members that had included drinking and dancing in a bar in Argostoli. McNamara’s family, he said, were now looking for “appropriate answers” to a death no one had expected.

Port authority police in Kefalonia have confirmed they were studying the yacht’s security camera system and photographs and messages on McNamara’s phone.