The story of the statue on top of the Brooklyn Bridge building could be intertwined with the overall story of the bridge. The bridge was a huge engineering feat. The statue might be there to signify the grandeur of the project. It could have been a gift from a community or an artist to mark the significance of the bridge. There could be a local legend or historical account about how it came to be there, but without delving into historical archives, it's hard to say for sure.
The Brooklyn Bridge is an iconic structure. If there's a statue on top of its building, it might have multiple interpretations. It could be a representation of the spirit of the city during the time of construction. It might have been inspired by the architecture and art trends of that era. Also, it could be a symbol of the connection that the bridge creates, not just physically between two places but also symbolically between different aspects of the city's life. However, more research would be needed to uncover the exact story behind it.