Mother-of-two Jean Campbell, 53, was last seen walking her dog and heading towards Cranhill Park in the East End of Glasgow last Friday night.
Her body was discovered the next day by her husband who was out searching for her. She is said to have suffered a particularly violent assault.
Officers were in the park last night to speak to people and distribute leaflets, appealing for information from anyone who saw Mrs Campbell leading up to her death.
Detective Chief Inspector Colin Carey said: "It is essential that we piece together her last movements."