In current resilience assessment frameworks for power distribution systems, the failure events of overhead structures e.g. utility poles are assumed independent. Since adjacent poles have similarities in wind exposure, age, rate of decay, and structural properties, among others, it is likely that a level of correlation exists between their failure events. To explore potential effects, here correlations among failure events of poles are considered in the simulation process using dichotomized Gaussian method (DGM) that generates correlated failure and survival events. A real distribution network in southeast of U.S. is chosen for the case study. The network consists of three substations with 7051 poles. Following realizations of the physical state of the infrastructure, connectivity based analyses are performed to estimate the number of customers without power considering time-dependent restoration sequences. Results indicate that correlations among failure events of poles have a noticeable impact on the resilience of the power systemneglecting this characteristic results in an error in the estimation of resilience of distribution systems. This may lead to risk management solutions such as maintenance and replacement of utility poles that are not optimal for resilience enhancement purposes