Emergency services were called out to the Cliffe block in Stannington Road, Stannington, at 7.15am this morning after reports of a man's body being found outside the 15 storey complex.
The circumstances are still under investigation but residents suggested the man had plunged from a 13th storey flat where a broken window was visible this morning.
The incident comes just 18 months since a woman aged in her 50s died after being found injured close to the scene.
Police said there are not believed to be any suspicious circumstances and there is no suggestion at this point from the authorities that the man fell to his death.
But after two tragedies in under two years at the council housing complex, residents who live nearby are calling for the authority to introduce better safety measures as a precaution.
They claim the windows open out too far and pose a potential risk to people living inside.
A 56-year-old man, who did not want to be named, said: "The windows swing right open, you could easily fall through it.
"And I know of kids getting into the building and going up onto the roof. It is extremely high so it is potentially dangerous.
"I think the council did put barriers up to stop that but they need to put their hand in their pocket again and look at the windows now."
Another woman, who lives across from the flats in Deer Park Road, added: "There were three or four police cars and an ambulance there and it was all cordoned off.
"Everyone was wondering what had happened. The block has been there for years and years.
"They need something doing to them. This has happened a couple of times now."
Matt Bell posted to Facebook: "If this is an accident then action must be taken on this block of flats to protect the current tenants."
Terry Marshall added: "I used to live in them. There are safety features on the windows but they open all the way around for cleaning, etc."
A South Yorkshire Police spokeswoman said: "Emergency services were called at around 7.15am this morning following reports a man had died in the Stannington area of Sheffield.
"An investigation is underway and in the early stages, but at this time there are not thought to be any suspicious circumstances."
Sheffield Council has been contacted for comment and we are awaiting a reply.