Is Castillo de Chapultepec haunted?
Mexico Reported haunting level 2 of 5

What actually happened
United States troops stormed the castle on 13 September 1847 in the assault that closed the Mexican-American War, with heavy Mexican casualties among its defenders.
The history
Begun in 1785 under Viceroy Bernardo de Gálvez, the palace became a military college in 1833, the residence of Emperor Maximilian and Carlota from 1864, and the National Museum of History, which opened on 27 September 1944.
What people report
Local tradition holds that Empress Carlota and the cadets who died in 1847 still walk the Alcázar terraces, and night guards have reported figures in the galleries.
That paragraph is reported tradition, not a claim about what is there. The history above it is sourced; the stories are recorded because people tell them.
Visiting
Primera Sección del Bosque de Chapultepec, Miguel Hidalgo, 11580 Ciudad de México, Mexico