A police cordon remains in place around the perimeter of the Redcourt apartments in Armley this afternoon as officers continue their murder investigation.
Neighbours of the woman found dead in Athlone Grove yesterday have spoken of their shock.
People living inside the apartment block where the woman was found had to identify themselves to officers before being let into their homes today.
West Yorkshire Police were called to the incident just after 9.30am yesterday. A forensics team arrived in the afternoon.
Police later arrested a man, who had fallen from a footbridge around 10am near the city centre, on suspicion of murder.
Kamil, a 26-year-old man who lives in the apartments, said: “I am really shocked. This is a quiet building, it’s why I like living here. It’s mainly young people, a mix of English and eastern Europeans.”
Another said: “There isn’t normally trouble here.”
Levi, 21, who lives on Back Athlone Grove, said: “It is shocking. I was stuck in the traffic yesterday on the way home from the city centre and we came home to see this.”
A man living in a street nearby, who did not want to be named, said: “It is too close for comfort.”
The woman’s family have been informed of her death.
West Yorkshire Police said in a statement last night that the man was still receiving treatment in hospital under police guard.
A spokesman added: “Anyone who witnessed anything suspicious in Athlone Grove in the time leading up to when the woman was found, or who saw the man on the footbridge prior to the fall, is asked to contact the West Yorkshire Police Homicide and Major Enquiry Team via 101 quoting Operation Pettywood.
“Information can also be given anonymously to the independent Crimestoppers charity on 0800 555 111.”