Police say 18-year-old Dominique Tombeau was caught spray painting the statue on 31 Chambers Street at 2:40 a.m. Tuesday.
Tombeau has been charged with making graffiti, resisting arrest, obstructing governmental administration, criminal mischief, reckless endangerment, criminal tampering and disorderly conduct.
The arrest may have prompted protesters to move from a park next to City Hall into Centre Street, where they remained for hours until police pushed them back shortly before 6 a.m.
An Eyewitness News camera showed police in riot gear pushing the protesters back.
The demonstrators have been camping out for about a week in City Hall Park, demanding the city defund the NYPD after the police killing of George Floyd in Minneapolis.
After the protesters were pushed back into the small park, police removed some of the metal barricades that protesters may have been using. Officers also removed several large umbrellas protesters had hoisted over an NYPD surveillance camera.
Police Commissioner Dermot Shea said there were "incidents of vandalism," "graffiti on some of the statues" and "attempts to damage some cameras" used by police.
Officers arrested a man they say punched an officer in the face and head with his fist around 5:45 a.m. Joseph Konnaris, 20, of Queens, is charged with assault, menacing, disorderly conduct and harassment.
A third arrest, for disorderly conduct, is pending.
The tension in front of City Hall came on the day New York City Council voted to approve a city budget plan that includes a massive funding cut to the NYPD.
Overall, the proposed budget calls for more than $6 billion in cuts citywide.
Mayor Bill de Blasio says $1 billion of that will come from the NYPD.
But critics say much of those cuts are nothing more than budgetary tricks.
To put all of this in perspective, New York City's $87 billion budget is still $14 billion more than the city budgeted just seven years ago.
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