* "The Brooklyn Bridge: A History" by David McCullough: This is a non-fiction book that tells the true story of the construction of the Brooklyn Bridge.
* "Brooklyn Bridge" by Colm Tóibín: This is a novel that tells the story of a young Irish woman who emigrates to America in the 1950s. The Brooklyn Bridge is a backdrop to her experiences, but the book is not explicitly about the bridge's construction.
So, depending on which book you're referring to, it could be either non-fiction or historical fiction.
To get a more accurate answer, please tell me the author of the book you're interested in.