75-year-old Miriam Burns was found beaten to death at her home near Killarney last Monday afternoon.
A man in his 50s was arrested on suspicion of her murder, but was released without charge and a file will be sent to the DPP.
Southern correspondent with The Irish Sun, Ann Mooney, says forensics could prove crucial in the case:
"Gardaí are awaiting the results of the intensive forensic examinations that they've done on both Miriam's house and the clothes that they found in a wishing well and in grounds near Ross Castle. The clothes actually were found after the main suspect who was being questioned and Killarney Garda station at the time told Gardaí that they were there."
