The victim in the Morton Gardens murder investigation has been named as 34-year-old Shana Tanesia Cover.
Her body was discovered in her flat in Morton Gardens on Thursday afternoon (August 21) after concern was raised for her welfare.
Warwickshire Police subsequently launched a murder inquiry.
Officers are appealing for information as they try to piece together the events leading up to Shana’s death.
A 50-year-old man from Rugby was arrested later the same day on suspicion of murder and has since been released on police bail.
Detective Chief Inspector James Essex, who is leading the investigation, said: “We are currently investigating several lines of inquiry in relation to Shana’s death and we are eager to speak to anyone who has information that may help us.
“The last reported sighting of Shana was on Thursday August 14 and she was found dead a week later.
“We need to try and account for her movements and whereabouts during this seven day period. Any information, no matter how small may be vital in helping us to build up a picture of her final movements.
“Incidents such as this are extremely rare and we have a dedicated team working on the case to ensure that whoever is responsible for Shana’s death is brought to justice as quickly as possible.
“The thoughts of the whole investigation team are with the friends and family of Shana at this time.”
An incident room has been set at Rugby Police Station. If you can provide information, contact the Major Investigation Unit on 01788 853956. Alternatively, if you would like to provide information anonymously, call Crimestoppers on 0800 555 111 or go to www.crimestoppers-uk.org.