MELBOURNE, Australia — The case is cloaked in mystery.In June, the bodies of two young Saudi sisters were found in separate bedrooms of the apartment they shared in Sydney, Australia. The remains had gone undiscovered for a month. There were no visible signs of injury, and the home showed no sign of forced entry. The police deemed the deaths suspicious.Nearly two months after the discovery, the authorities still know little about the women, even after an extensive investigation in which they spoke to many people in the neighborhood. The women, the police said, “seemed to keep to themselves.” It also remains unclear how they died, though an autopsy has been performed.Stymied, the police took another step this week in hopes of finding new clues: They revealed the identities of the women as Asra Abdullah Alsehli, 24, and Amaal Abdullah Alsehli, 23. The sisters arrived in Australia from Saudi Arabia in 2017, the police said.“We’re appealing for information because we don’t know a lot about the girls,” Detective Inspector Claudia Allcroft said at a news conference. The case is unusual, she said, because the cause of death remains unknown, and the women “were 23 and 24 years old, and they have died together in their home.”Speculation has abounded over the sisters’ lives and deaths. Local media posited that the women could have been seeking asylum in Australia. If so, it would be an echo of a case of two Saudi sisters in New York, whose bodies were found in 2018 on the bank of the Hudson River. Their deaths were ruled a suicide; they had requested asylum in the United States, the police said, and had said they would rather kill themselves than return to Saudi Arabia.In the Australian case, workers in the women’s building said they were secretive and seemed nervous and scared, according to The Sydney Morning Herald. The women had told the building manager that they thought someone was tampering with their food deliveries.The police declined to answer questions about the sisters’ citizenship or asylum status. Detective Allcroft said that there was no information indicating that the sisters had tried to flee Saudi Arabia, and that the women’s family in their home country, who are helping with the investigation, were not under suspicion.In March, the authorities conducted a welfare check on the sisters after the building manager became concerned about them, reporting that their food had been left out in the apartment building’s common spaces. At that point, Detective Allcroft said, “they appeared fine, and there was no further action from police required at that stage.”The police were called to the apartment for another welfare check on June 7 and found the sisters’ bodies. That call from the landlord came after the sisters had failed to pay rent, according to local media.A post-mortem examination was conducted on June 9 and 10, but the coroner has not handed down a finding, the police said. Toxicology results are also pending.