They said Joseph's body, found at her apartment on the Versova-Juhu Link Road, was shifted to the Nanavati hospital mortuary in north Mumbai.
Joseph, who won the Miss India title in 1997, had worked as a model and had been involved in activities related to animal rights.
Police said that she was supposed to marry businessman Gautam Khanduja later this year and that some problems between them may have led to her death.