Object-centric processes involve a substantial number of object instances that may be in different states during runtime. In addition, there are numerous dependencies between the states of these object instances. Inter-object constraints can organise these complex, nested dependencies by documenting and controlling them using a higher-level process. To examine the correct runtime behaviour of such process instances, a comparison is made between the event log and the defined inter-object constraints. Conformance checking is thereby used to determine the fitness value. Identifying deviations from these dependencies is crucial for verifying the correct execution of the entire process. This paper proposes a methodology for conformance checking of inter-object constraints based on linear temporal logic rules. The developed approach is evaluated in three different scenarios. The findings demonstrate that the proposed approach constitutes a reliable method for the conformance checking of inter-object constraints.