In a Wireless Sensor Network (WSN) where the sensors monitor the environment to the purpose of raising alarms about the occurrence of some events, we consider the problem of detecting false alarms (i.e. false positives). We adopt a system level diagnosys model, where all the sensors in the region where the alarms have been raised cooperate to execute mutual tests. The test outcomes are given as input to a diagnosis algorithm that identifies the faulty sensors and thus confirms or neglects the alarm. The diagnosis algorithm can succeed in this work if the tests among sensors are sufficient to achieve a given diagnosability of the system, that depends on topological properties of the WSN. This work considers the problem of determining a test strategy of the sensors in a WSN in order to ensure that the desired system diagnosability is met. In particular it is shown by simulation that appropriate testing strategies are successful to guarantee given levels of system diagnosabilities depending of the network topology or its density.