It follows claims that onlookers urged the man to jump from the new Southwater 1 car park in Telford Town Centre.
Police criticised their behaviour as "appalling" and said it hampered the operation to make the scene safe and officers attempts to speak to the man.
The tragedy happened on Saturday afternoon when the town was busy with shoppers.
Witnesses took to social media to describe how people on the ground goaded the man to jump.
Police were called to the scene at 1.10pm, and negotiators spoke with the man, but unfortunately he fell from the car park and was pronounced dead at around 3.40pm.
Detective Sergeant Mark O'Connor, from West Mercia Police, said: "Following the tragic incident at the multi-storey car park at Southwater on Saturday, it has been brought to our attention of the distasteful and disrespectful actions and comments upon social media at the time and subsequent to the incident.
"We do not condone such behaviour, and would hope that the local community would work with our officers to provide information regarding those who committed the cruel taunts, this was clearly someone who was in need of support.
"In response to the activity on social media, the origin of any comments or material that is deemed to be unlawful will be investigated and appropriate police action will be taken against any identified individual.
"I would urge that any person who is in possession of any related material does not publish it any further and ensure it is disposed of.
"We would remind those to be respectful and think of the family and friends at this sad time."
The man had not yet to be formally identified yesterday and the investigation was referred to the coroner.
On the Shropshire Star Facebook page, one witness Moira O'Reilly Shrimpton, said: "I read a status yesterday from someone who was upset because she "shouldn't have had to witness it". She didn't have to.
"She should have left the area and let whoever was trying to help the man to do their job without adding to the crowd.
"I was in the rink and had to walk through Southwater to get there. I was gobsmacked by the amount of people with their phones out. Shameful behaviour."
Nigel Newman, spokesman for Telford & Wrekin Council, which owns the site, said: "Our thoughts are with the family and friends of the man who died at Southwater.
"On the upper tier of the car park there is perimeter fencing approx 6ft high which is topped with security wire."
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