When using LevelDB as the state database in Hyperledger Fabric, there is no specific schema that the data stored in the ledger needs to adhere to. LevelDB is a key-value store, which does not enforce any schema on the data it holds. This flexibility allows applications to define their own formats and structures for the data they store, which can vary from simple strings and numbers to more complex serialized data structures. This schema-less nature of LevelDB enables developers to implement the data handling that best suits their application's needs without the constraints of a predefined database schema.