The historic McKim Building at the Copley Square headquarters of the Boston Public Library was painted with graffiti overnight, leaving about $2,000 worth of damage as workers labored into the afternoon to remove the paint.

Officials said the building has been sprayed with graffiti in the past, but the latest incident was considered unprecedented because of the scale. Using mostly white paint, somebody painted along the entire wall of the McKim building facade on Dartmouth Street, officials said.

“This is a public building, free to all,’’ said Melina Schuler, spokeswoman for the library system. “To have it tagged and damaged in this way is really unfortunate. This is a place where the public learns and comes to spend time.’’

According to Boston police, officers responded to Copley Square around midnight to investigate a report of vandalism in progress.

The person suspected of “tagging’’ the library was described as a black man wearing a black hoodie with a red hat and backpack, according to Rachel McGuire, a Boston police spokeswoman said.

Police are checking nearby surveillance cameras for information about the person as part of the ongoing investigation.

Schuler said four “graffiti busters’’ from Boston City Hall worked with six library staffers to wash the paint from the building.

John R. Ellement can be reached at ellement@globe.com. Follow him on Twitter @JREbosglobe.