FPGA that exploits via-switches, which are a kind of non-volatile resistive RAMs, for crossbar implementation is attracting attention due to its high integration density and energy efficiency. Via-switch crossbar is responsible for the signal routing in the interconnections by changing on/off-states of via-switches. To verify the via-switch crossbar functionality after manufacturing, fault testing that checks whether we can turn on/off via-switches normally is essential. This paper confirms that a general differential pair comparator successfully discriminates on/off-states of via-switches, and clarifies fault modes of a via-switch by transistor-level SPICE simulation that injects stuck-on/off faults to atom switch and varistor, where a via-switch consists of two atom switches and two varistors. We then propose a fault diagnosis methodology for via-switches in the crossbar that diagnoses the fault modes according to the comparator response difference between the normal and faulty via-switches. The proposed method achieves 100% fault detection by checking the comparator responses after turning on/off the via-switch. In case that the number of faulty components in a via-switch is one, the ratio of the fault diagnosis, which exactly identifies the faulty varistor and atom switch inside the faulty via-switch, is 100%, and in case of up to two faults, the fault diagnosis ratio is 79%.