Television footage showed uniformed men inspecting the wreckage of the chopper on top of the building, which was also partly damaged by the impact.
"The incident happened during basic flight training for unknown reasons and a special team is investigating the cause," an official told reporters.
Taiwan in November took delivery of its first six AH-64E Apache attack helicopters bought from the United States as it modernises its military despite warming ties with China.
It temporarily grounded the choppers from December to February for checks after Washington warned the model could malfunction.
The Taiwanese army is the first force outside the US to use the Apache AH-64E, the latest variant of what is described as the world's most powerful attack helicopter.
Taiwan ordered 30 Apache helicopters, the remainder of which will be delivered by the end of 2014. The order was part of a $6.5 billion arms deal unveiled in 2008 that irked Beijing.