Today's von Neumann computing systems are facing major challenges making them not suitable for evolving ultralow power (e.g., edge computing) applications. Therefore, alternative architectures that make use of post-CMOS devices are under investigation. One of these architectures is computation-in-memory (CIM) based on memristive devices; it performs (parallel) computing within the memory core, which prevents data-movement and results in low energy consumption, at the cost of some modification in memory design. Hence, a CIM die can work either in memory configuration or in computation configuration. One implementation of this architecture is based on Scouting logic; it allows the execution of logic operations within the memory. This paper discusses fault modeling and testing of CIM architectures, applied to a Scouting logic-based architecture. It demonstrates that unique faults can occur in the CIM die while in the computation configuration, and that these faults cannot be detected by just testing the CIM die in the memory configuration, thus leading to test escapes. The paper demonstrates how an efficient test can be developed that detects all faults in both configurations. Moreover, it shows that testing the die in the computation configuration reduces the overall test time while improving the outgoing product quality.