Detective Chief Inspector Alex Campbell said: “This has been a hugely distressing incident, not least for the family and friends of Rita but also the wider community.
“Rita’s family would be extremely grateful for any information that can be offered, and would like to request privacy at this difficult time.”.
Sussex Police are asking locals to check their bins and gardens for the missing axe and a navy blue North Face rucksack.
They said: "Rita was a much loved member of the community and was adored by her family and friends.
Rita Lambourne, 58, suffered catastrophic injuries at her home in Bexhill, East Sussex, on February 12.