WASHINGTON — Police said they are investigating whether a woman arrested in the splattering of green paint inside two chapels at the Washington National Cathedral has any connection to two similar incidents on the National Mall.

Jiamei Tian, 58, was arrested Monday inside the cathedral shortly after the paint was found and charged with defacing property, police and cathedral officials said. Investigators were hoping to question her about the vandalism on the Mall, including the splattering of green paint at the Lincoln Memorial, but a language barrier was complicating those efforts, Assistant D.C. Police Chief Peter Newsham said after the arrest.

It was not immediately clear if Tian had an attorney. Police believed she was homeless. No motive was given.

Green paint was found early Friday morning on the Lincoln Memorial, and symbols have also been found painted in green on another statue on the Mall. The Lincoln Memorial was closed temporarily but reopened later Friday.

Sgt. Paul Brooks, a U.S. Park Police spokesman, said it was too early to tell whether the same person was responsible for the vandalism at the two Mall landmarks. He noted that while the paint appeared to be splattered indiscriminately on the memorial, the statue appeared to have been deliberately painted. The symbols on the statue were not immediately decipherable.

Officials at the cathedral discovered the paint inside two chapels Monday afternoon. It was still wet, which led them to believe the vandalism had just occurred. Officials called police immediately and closed the cathedral to visitors while authorities searched the grounds. The paint was splashed onto an organ and on the floor inside the cathedral’s historic Bethlehem Chapel on the basement level, officials said. It was also found inside Children’s Chapel in the nave of the cathedral.

Also Monday, U.S. Park Police said green paint was found on the statue of Joseph Henry outside the headquarters of the Smithsonian Institution on the Mall. Henry was the Smithsonian’s first secretary.

Meanwhile, crews continued working Monday to remove the paint from the Lincoln Memorial. The National Park Service said progressively stronger substances would be used until all the paint is gone, which could take several days. The memorial was scheduled to be power washed Tuesday.

Cleanup and restoration work at the cathedral was expected to cost $15,000, cathedral spokesman Richard Weinberg said. Crews were there late Monday, and events at the cathedral were going on as scheduled. Some of the paint was splattered onto the decorative wall behind the altar in the Children’s Chapel, which has ornate wood carvings that required some restoration, Weinberg said.

Bethlehem Chapel was opened in 1912 and is the oldest section of the cathedral. It was the site of President Woodrow Wilson’s burial rites, and his remains were entombed there for more than three decades. Wilson’s remains were later interred in a memorial bay on the cathedral’s main level.

Washington National Cathedral is an Episcopal cathedral that serves as the nation’s spiritual home. It has hosted inaugural prayer services and the state funerals for presidents Dwight Eisenhower, Ronald Reagan and Gerald Ford.