The Himachal Road Transport Corporation (HRTC) bus, carrying 36 passengers, was travelling from Jhakri to Dharamshala, they said.
One person died on the spot while two others died during the rescue operations,Director General of Police Somesh Goyal said.
Six people, who were seriously injured, were taken to the Indira Gandhi Medical College here while 12 others were undergoing treatment at the Community Health Centre (CHC) in Kumarsein, he said.
The death toll may rise as six people are in a critical condition, they said, adding investigations are on to ascertain the cause of the accident.