Hexagonal boron nitride (h-BN) has emerged as a promising 2D/layered dielectric owing to its successful integration with graphene and other 2D materials, although a coherent picture of the overall dielectric breakdown mechanism in h-BN is yet to emerge. Here, we have carried out a systematic study using conduction atomic force microscopy to provide insights into the process of defect generation and dielectric degradation in the progressive breakdown (PBD) and hard breakdown (HBD) stages in 2−5 nm thick chemical vapor deposition (CVD)-grown multilayer h-BN films. The PBD and HBD regimes show different behaviors. Under electrical stress in the PBD stage, defects are generated progressively in the h-BN, leading to a gradual reduction of the effective barrier resistance and continuous soft breakdowns (SBDs) of the dielectric material. Random telegraph noise nano-spectroscopy shows that low frequency noise becomes dominant after an SBD event due to the creation of additional defects around the percolation path. We also observe a wide variation in the current−voltage (I−V) breakdown plots in the PBD stage, giving rise to non-Weibull statistical distribution of the breakdown voltage. We attribute this observation to the significant thickness inhomogeneity in the CVD films. At HBD, h-BN materials are always physically removed from the film, leading to the formation of pits at the breakdown location. Interestingly, pit formation is also occasionally observed in the PBD stage under very low current compliances, suggesting that breakdown may proceed by a mixture of defect generation and material removal in h-BN CVD films.