The bus fell off AH12 Highway last night and plunged into a 30-metre ravine in Muang district in Tak province, which borders Myanmar, they said.
The driver, who survived the mishap, was trying to overtake cars on a hilly road when the bus skidded off and tumbled before crashing into a tree, police said.
Twenty-eight passengers died on the spot while four others were pronounced dead at a hospital, they said.
Initial investigations showed that the passengers were local officials and the elderly from Tasailuad Tambon Municipality in Tak's Mae Sot district. The victims were en route to Ubon Ratchathani province and were to cross the border to Laos.
A WHO report recently noted that Thailand witnessed 38.1 road deaths per 100,000 people in 2010 - only behind the Dominican Republic in the Caribbean.