The body of a 48-year-old woman found by her daughter had been lying in her flat for several weeks after a severe beating, police have revealed.
Mother-of-one Charmaine Dempsey, who had massive injuries to her head and jaw, had a "troubled past", officers said.
Mrs Dempsey, 48, had not been seen for weeks and was discovered by her daughter at her one-bedroom flat in Ivory Walk, Bewbush, Crawley.
Police believe Mrs Dempsey died more than a month ago.
Police launched a murder inquiry after a post mortem revealed she died from severe blows to the head and chest.
Detective Chief Inspector Tony O'Donnell said "Mrs Dempsey had a troubled past and was a colourful character who liked a drink.
"The fact that she was not found for so long over the Christmas period is very sad for her and for society. We hope that by speaking to her associates we may be able to identify a motive, which remains unclear."
He said Mrs Dempsey's family and friends were devastated.
"This was a horrible attack and we are determined to bring the culprit to justice," he said.
"Mrs Dempsey had a small group of friends who would visit her regularly and we need to speak to them all.
"We want to speak to anyone who had seen Mrs Dempsey and knows of her last movements, anyone who saw anything suspicious at her home, or anyone who may have spoken with Ms Dempsey recently and certainly within the last four to six weeks."
Neighbours in Ivory Walk said the murdered woman had lived in the small council block of flats for about two years.
Ian Byrne, who lives opposite, said: "She was a perfect neighbour. She kept herself to herself."
Mrs Dempsey, who was unemployed, was living with a regular partner until his death in August.
Police are refusing to say whether a weapon was used in the killing saying only the injuries were very severe.
The body had decomposed, making it harder for forensic experts to work out what had happened.
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