The body of Kathleen Grundy, who died on 24 June, was exhumed on 1 August and a post-mortem examination was carried out after her daughter and grandsons raised concerns about the contents of her will.
Mrs Grundy, the widow of a former mayor of Hyde, Greater Manchester, was said to be devoted to her grandsons but is understood not to have left them anything.
Detectives are now examining the circumstances of her death and have said they may also be looking at the deaths of 19 other patients of her GP, Dr Harold Shipman, also of Hyde. They are waiting for the results of forensic tests on the body of Mrs Grundy before deciding whether to interview the doctor.
A spokesman for Greater Manchester Police said there was nothing to suggest anything suspicious in any of the deaths.
"We are investigating the circumstances surrounding Mrs Grundy's death after some concerns were raised by the family," he said.
The body of Mrs Grundy, who died unexpectedly, was found at her home after she failed to turn up at a luncheon club.
Mrs Grundy, whose husband John, a former mayor of Hyde, died 30 years ago, was described as a sprightly woman who was actively involved in working for charities, including Age Concern.
Dr Shipman, who has been a doctor for 28 years, refused to comment yesterday. A spokesman for the Medical Defence Union, which is advising him, said: "Due to Dr Shipman's duty of confidentiality he cannot discuss the treatment of any of his patients."
Friends of Mrs Grundy expressed their shock at her death. Geoffrey Ridgway, a friend of 34 years, who lives in a cottage owned by Mrs Grundy, said: "She was the last person we expected to go. She loved her gardening and watching sport and she thought the world of her family."
A neighbour Madeleine Oldham said: "Just before she died she heard her grandson had passed his law degree and she was ever so proud of him. This is so sad."Reuse content