Abstract We extend ontology-based data access with integrity constraints over both the source and target schemas. The relevant reasoning problems in this setting are constraint satisfaction—to check whether a database satisfifies the target constraints given the mappings and the ontology—and sourceto-target (resp., target-to-source) constraint implication, which is to check whether a target constraint (resp., a source constraint) is satisfified by each database satisfying the source constraints (resp., the target constraints). We establish decidability and complexity bounds for all these problems in the case where ontologies are expressed in DL-LiteR and constraints range from functional dependencies to disjunctive tuple-generating dependencies