Story highlights Police say they're arrested a 58-year-old woman in the National Cathedral incident

Green paint was found at the National Cathedral and on a Smithsonian statue

The discoveries come three days after similar paint was found on the Lincoln Memorial

Officials aren't sure whether the incidents are related

Police in the nation's capital have arrested a woman in connection with the splattering of paint in two locations inside the National Cathedral, a Washington Metropolitan Police Department spokesman said.

Jia Mei Tian, 58, was charged with defacing property. When officers arrested he on Monday, she had green paint on her clothes and shoes, and paint cans were found in three bags she had with her, according to a police report obtained by CNN.

Officials said it was not clear whether the paint discovered Monday at the National Cathedral and on a statue outside the Smithsonian Castle was related to the incident last week at the Lincoln Memorial , though all three locations were marred with green paint.

The arrest of the woman was related only to the National Cathedral incidents.

The police report said that her clothes were sent to a forensics team to determine if the paint on them matches the paint at the other locations.

A fourth landmark in Washington -- Luther Place Memorial Church -- was also found with green paint last week, but police did not link that incident to the others.

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Jack Reiffer, the parish administrator at the church, said the paint was splattered on a statue of the 16th century Protestant reformer Martin Luther.

White paint mixed with feces was also found splattered on the front of the church's organ, and up onto the organ pipes and the chairs where the choir sits. Some of the mixture also got on the floor.

At the cathedral, in Washington's Northwest quadrant, the paint was discovered splattered on an organ console and casework inside the historic Bethlehem Chapel, in the building's lower level.

A spokesman said the paint was wet when it was discovered. Paint was also found in the Children's Chapel, in the cathedral's nave.

The cathedral is a popular tourist destination.

Five miles south, on the National Mall, green paint was discovered on the statue outside the Smithsonian Institution Building, known widely as the Castle.

Linda St. Thomas, the Smithsonian's chief spokeswoman, said the statue is of Joseph Henry, the first secretary of the federally administered group of museums.

St. Thomas said that the paint appeared similar to that found on the Lincoln Memorial and that the U.S. Park Police, which manage the National Mall, were determining whether the paint was the same.

It wasn't immediately clear when the paint discovered at the Smithsonian Castle was found. St. Thomas said security guards first noticed it on Sunday afternoon, while Park Police Sgt. Paul Brooks said it was first reported Friday.