They have urged parents to speak to their children about the dangers of climbing onto roofs, especially asbestos roofs which can be extremely brittle and can bear little weight.
And officers say school teachers could also help to reinforce the message to pupils that climbing onto structures could result in injury or potential death.
PSNI Magherafelt say the incident happened in Castledawson Tuesday.”
An officer wrote on Facebook: “We almost had a crew delivering a death message there.
“Kids just over the age of 10 decided to climb on the roof of an industrial building in Castledawson.
“The asbestos roof – over 30ft off the ground – gave way.
“The kids went partially through the roof.
“Now we aren’t going to be all holier than thou and pretend we didn’t climb trees or explore places when we were younger, but parents we would strongly ask you have a word with your kids.
“Teachers you can help too and tell your class.
“Aside from the fact these places are private property and there are a rake of trespass and criminal damage offences.
“Explain to them the absolute craziness of climbing on roofs – old asbestos roofs are especially brittle and can just about take the weight of a cat.
“A child has no chance.
“Spread the word and lets not have a repeat of this one, that was far too close for comfort.”