Police in the Bahamas are deepening their investigation into an alleged plot to extort up to $25m from Hollywood star John Travolta over the death of his 16-year-old son.

A prominent politician on the island of Grand Bahama, Pleasant Bridgewater, quit as a member of the Bahamas senate over the weekend, and investigators questioned a former tourism minister who had claimed to be a close friend of the Travoltas.

Sixteen-year-old Jett Travolta was found unconscious in a bathroom at the family’s holiday home on the island on 2 January, and hospital authorities concluded he died of a seizure.

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Tarino Lightbourne, a paramedic who said he tried to revive him is still in custody, on suspicion of being part of an extortion plot, although neither the local police nor Mr Travolta’s lawyers have released details of the alleged scam.

Early reports suggested that Mr Lightbourne and others had been trying to get money in return for suppressing a photo of the 16-year-old just before he died, but conflicting accounts are now circulating in the island of 75,000 people.

The former tourism minister, Obie Wilchcombe, was questioned by police last Friday, it has emerged. He was involved in a negotiation with Mr Travolta’s lawyers which, according to some allegations, demanded payments of between $10m and $25m. He was released without charge.

Mr Wilchcombe, a close friend of the Saturday Night Fever and Pulp Fiction star, made a round of television appearances in the days after the tragedy death, saying he had been with the family in the hours after his son’s death.

On CNN’s Larry King Live, Mr Wilchcombe shared intimate details of the funeral home and the cremation of Jett Travolta.

Ms Bridgewater, a leading lawyer and politician in the island, angrily vowed to clear her name, as she submitted her resignation from the 16-member senate appointed by the Bahamas governor-general, the Queen’s representative. She had been acting as a lawyer, and the charges of extortion were “untrue and unfair”, Ms Bridgewater said.

"How these innocent actions can be so misconstrued, so perversely twisted to mean something other than it was, is a mystery," she said without providing more details.

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Ms Bridgewater is free on bail. The leader of the opposition party, former Prime Minister Perry Christie, said in a statement that he regrets the turn of events and accepted Ms Bridgewater’s resignation.

John Travolta and wife Kelly Preston have returned to the US with the remains of their son. The couple have said Jett became sick when he was two years old and was diagnosed with Kawasaki Syndrome, an illness that leads to inflamed blood vessels. They blamed household cleaners and fertilizers and said a detoxification program based on teachings from the Church of Scientology helped improve his health. Outsiders have repeatedly claimed that Jett exhibited signs of autism, a condition which the Church of Scientology does not recognise.

The couple said at the time of his death that they were "heartbroken that our time with him was so brief".

Jett was the couple’s only son. They have a daughter, eight-year-old Ella Bleu.

Last week, the Travolta family sparked a mystery by filing their extortion plot, saying: “Regrettably, in a time of such terrible grief, there are often a few individuals who attempt to make false claims in hopes of making millions of dollars. We will never let that happen."

Reports today suggested that family lawyers had entered negotiations with the people involved in the plot, in order to help gather evidence.