Police have sealed off a section of a communal garden as part of an ongoing investigation in the Logie area.
Residents on Colinton Place described seeing a large police presence at the scene from 1am this morning.
One officer is currently guarding the rear exit of one of the blocks whilst CID carry out door-to-door inquiries.
One woman said CID had asked her if she was aware of an incident on the ground floor.
Another man who declined to be named said there was around 10 police officers at the scene.
He added: “I saw the vehicles stationed on Saggar Street just after 1am.
“The officers were in the area that was cordoned off. We are none the wiser as to what has actually happened.”
Some nearby residents had asked locals if there was any cause to be alarmed as he saw the police cordon.
Police Scotland have been approached for comment.