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The police have confirmed that Zsuzsanna Besenyei knew the 54-year-old man that has been arrested on suspicion of her murder.
Zsuzsanna (37) was found dead on the sand at La Pulec beach in St Ouen on 16 May and was formally identified yesterday following DNA analysis.
Detective Superintendent Stewart Gull, Head of Crime Services, said the police were unable to "go into specifics" but confirmed they're treating Zsuzsanna's death as a homicide.
A man was arrested in St. Helier on Friday at 06:34. While Mr Gull said the man was the only suspect at the moment, the police were keeping "an open mind about the involvement of other parties."
Zsuzsanna's cause of death still hasn't been identified. A Home Office Registered pathologist flew to the island last Friday to carry out a post mortem examination which came back inconclusive.
Video: An islander spotted Zsuzsanna's car in St. Aubin's Bay as the tide was going out.
Mr Gull also said that Zsuzsanna's car, a blue Ford Fiesta Ghia with the registration number J48188, was found fully submerged in water, 500 metres away from La Haule slip in St. Brelade. He said the car had been driven into St. Aubin's Bay at low tide.
Officers haven't been able to determine when Zsuzsanna died and Mr Gull urged anyone who may have seen her after 10 May to contact the police. He said: "It is important to establish the timeline of her activities. There are big gaps. We are a small island, it's a small community, someone must have seen her or her car."
Pictured: Zsuzsanna's car was found fully submerged in water, 500 metres away from La Haule slip in St. Brelade.
Zsuzsanna was last seen on the evening of Thursday 10 May but the police say someone might have seen Zsuzsanna in St. Helier on Friday 11 May. DI Craig Jackson said earlier this week that the police are particularly interested into piecing together Zsuzsanna's movements over the weekend of 12 and 13 May.
Up to 20 officers are now working on the investigation and on-going enquiries include elements of forensic, search, passive data, house-to-house and interviews.
Family Liaison Officers have also been appointed, including a Hungarian speaker, who is working to support the family in Hungary. Mr Gull said that, while Zsuzsanna had been living in Jersey for seven or eight years, she had no immediate family In the island.
Anyone with information can contact the police on 612612 or Crimestoppers anonymously on 0800 555 111.
Video: Detective Superintendent Stewart Gull, Head of Crime Services.
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