Awhile ago at work I was half asked, half told to find a connection between the park and the American Civil War in order to commemorate its sesquicentennial. I'm not a Civil War historian, which makes finding non-obvious connections within this hugely dense topic of history difficult. Bryant Park, then known as Reservoir Square, was most likely used as an encampment for Union soldiers during the war, but I think that was true of most parks and public spaces in the city. Also, most of the confirmation of this comes from NYC guidebooks, not actual primary sources. I did find a small connection via one of my favorite monuments in the park.
At the east end of the reading room stands a monument to William Earle Dodge, founding member of the American chapter of the Y.M.C.A., New York 8th District Congressman from 1866-1867, and Native American rights activist, among many other things.
Though Dodge left the service in June1863, he returned to volunteer with the U.S. Army to restore order in the city during the Draft Riots under Major General John Z. Wool. Transcripts of Wool's reports are available online. The Draft Riots, still considered one of the largest (and by day three) heinous acts of civil disobedience in the country, waged on for four days throughout the city from July 13 - July 16, 1863. The African-American community was especially targeted and horribly mistreated, leading to an exodus from the city by that community, which I'm sure had a huge impact on New York City's cultural and social development in the following decades.