Is Shaniwar Wada haunted?
India Reported haunting level 4 of 5

What actually happened
A devastating fire consumed the palace in 1828, leaving only its foundations, fortified walls and spiked gates standing.
The history
Peshwa Baji Rao I began the palace in 1732 as the seat of Maratha power; it was a seven-storey complex with five grand doors, teak carvings and the Hazari Karanje fountain.
What people report
The Ministry of Tourism itself notes the fort is said to be haunted after the assassination of Peshwa Narayanrao within its walls; local tradition tells of his cries for help on moonless nights.
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
Shivaji Road, Kasba Peth, Pune, Maharashtra 411001, India