The body of the 44-year-old man was discovered in shrubs outside the high-rise Hawthorn House flat building in the Heath Town area of Wolverhampton at around 5.30pm on Tuesday.
Police and paramedics were called to the scene off Clover Ley but the man was soon pronounced dead.
It is believed the body of the man, who lived in one of the nearby flats, may have been in the bushes for more than 24 hours before it was found.
A man has been arrested but police have not confirmed what he is suspected of, with the death being treated as unexplained.
Residents living in Hawthorn House were coming to terms with the news of the death on Wednesday as officers continued to search the area which was cordoned off with police tape.
One resident, who asked to remain anonymous, said she was sitting in her flat when she saw the blue lights arrive on Tuesday evening.
She said: "I went down to have a look and saw the police and ambulances all around the building, but didn't find out anything until this morning.
"I'm very shocked and scared about what has happened and don't know what to think about it.
"I hope it doesn't happen again around here as I have children and I really fear for them when things like this happen so close to home."
Another resident, who didn't want to be named, said she had been at work and was heading home when she got a phone call from her friend about the police presence.
She said: "I was on my way home when my friend who lives on the ground floor called and told me there were ambulances and even armed police outside the block, so I was shocked to hear that and then what had happened.
"This is normally a very quiet area and not a lot happens and we were even out on Saturday letting off fireworks for the children.
"It's just hard to believe that someone's died, especially someone living in this tower block."
A post mortem was due to be held on Wednesday to establish the cause of the man's death.
West Midlands Police has urged any witnesses or anyone who was near Hawthorne House since late morning on Tuesday and who may have seen anything to contact them.
Call the force on 101 or message on Live Chat via their website quoting log 3345 from 9/11.