The accident happened on a highway circling the city late yesterday for reasons still under investigation.
The official, who is with a regional branch of the Interior Ministry, requested anonymity because he was not authorized to speak on the record.
Six seriously injured passengers were taken to two hospitals in Alicante, news agency Europa Press reported, citing ministry officials. The other 32 were treated at the scene of the accident.
Europa Press quoted the Center for Emergency Information and Coordination for the region of Alicante as saying that the bus overturned but that no other vehicles appear to have been involved.