The murder of a 75-year-old widow in her home was "a vicious assault" on a defenceless victim, police said.
Mrs Vardey died from multiple injuries
Officers investigating the killing of Pamela Vardey said they were liaising with colleagues examining the murder of Nora Tait in Doncaster last year.
Det Supt Carl Sturgess added there was nothing yet to connect the attack on Mrs Vardey in Rotherham, to the unsolved murder of Nora Tait.
The body of Mrs Vardey, a lay preacher, was found on Sunday after a fire.
The pensioner was found dead by firefighters who were called to her burning dormer bungalow in Herringthorpe Valley Road.
'Defenceless elderly lady'
The officer said she had died from a multiple injuries to her whole body but had not been stabbed.
He added: "This was a vicious, sustained assault on a defenceless elderly lady."
Mr Sturgess said he had not yet established why Mrs Vardey was killed but his team were examining the possibility it was a burglary or robbery.
He said Mrs Vardey was a Methodist lay preacher and had visited a friend from Broom Lane Methodist Church at 1400 BST the day before she was found dead.
She left, saying she was going to get petrol, and her car was later found parked at home.
The weapon used to kill Nora Tait has never been found
The detectives asked for anyone in the area to contact him if they saw people calling at Mrs Vardey's home in recent days.
He added: "There is every possibility with the person or persons involved in this offence that their clothes will have been heavily bloodstained."
Mr Sturgess said he was convinced the fire was deliberately started by the intruders to conceal evidence.
He said Mrs Vardey lived alone and had no children. Her husband died in 1979.
Nora Tait was brutally beaten to death at her home in Hexthorpe, Doncaster, in October last year.
The 69-year-old had just bought a fish and chip supper when she was attacked and her uneaten meal was left on the table.