Theresa Jordan's body was discovered in bushes next to the boundary wall of the Asda store in Kimberley Road, Harehills, on 23 June.
Ms Jordan, known as Terri, was last seen on 11 June and officers have appealed for help to piece together her last movements.
They added: "Gone but not forgotten. We will see you again, this is not where it ends. We will carry you with us until we see you again. Rest in peace."
As part of their inquiries, police have also released a CCTV image of Ms Jordan which was taken on the day she went missing.
Det Supt Sarah Jones, of the Homicide and Major Enquiry Team, said: "The last confirmed sighting of Terri was on 11 June and we are keen to speak to anyone who may have seen her after, or has any information in respect of what she was doing after this time.
"We are also keen to speak to anyone who has been in the Kimberley Road area and witnessed anything suspicious or has information which may help with our investigation."
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