Andrea, 26, a mum of three, told her family she was going out to have a cigarette at the flat in Bell Green, Coventry.
Paramedics were called but were unable to save her and she was pronounced dead at the scene on Sunday night.
A woman who lives with her daughter opposite the family told the local news station: "People say that she fell from the tower block after going out for a cigarette. Apparently one of her children went out to find her and saw her body on the ground - it must have been terrifying for them.
"I knew Andrea to say hello to - she was always playing out on the grass with her children, she was such a good mum.
"She really looked after those little ones."
Flowers were left near the scene of the incident, including one which read: 'To mum, I love you so much. I will not forget you. From Sienna, Kia and Joshua'.
Andrea's mother also left a tribute to daughter, which said: "Words can't describe how I feel right now. You were taken from me so suddenly and I just wish so much I could have done something.
"I love you so much Andrea and I always will, Mum."
Detective Sargeant Paul Jones, from West Midlands Police said: "Police were alerted to the fall just after 9pm following a call from the ambulance service. It was clear nothing could be done to save the woman, 26, who was pronounced dead at the scene.
"The woman's next of kin have been informed and the matter referred to the coroner."