Is Old Government House haunted?
Australia Reported haunting level 4 of 5

What actually happened
Governor Denison handed the house to the Parramatta Park Trust in 1855, after which it served as a boarding house and school, with The King's School occupying it from 1910 to 1965.
The history
Built by convicts between 1799 and 1818, Old Government House served the first 10 governors of New South Wales as a country residence and is one of the 11 Australian Convict Sites on the World Heritage list.
What people report
The National Trust hosts Paranormal Nights at the house, and visitors on its ghost tours have reported sightings in the old residence.
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
Old Government House, Parramatta Park, Parramatta NSW 2150, Australia