In New York City (NYC), the early period of the COVID-19 pandemic in the spring of 2020 induced a significant shift in the use and accessibility of urban green spaces (UGS). To understand the impact of COVID-19 on the access to UGS, we conducted a spatial analysis of geographic access to UGS and perceived access based on data collected from a social survey deployed from May 13 to June 15, 2020. We examine geographical accessibility to UGS and how this compares to perceived accessibility, or the ease which residents feel they can access a UGS. We further explored the correlation between spatial access to UGS and fifteen social vulnerability variables including economic status, household composition, minority status, and housing type for different zip codes. The results show that geographical proximity variables can predict a number of the perceived access variables, particularly those related to COVID-19 measures. Although lower-income communities were found to have higher spatial access to UGS, many of the same communities, including people living in crowded and multi-unit buildings, on average only have access to smaller green spaces, suggesting an uneven distribution of larger quality parks. This observation is further confirmed by survey results. These findings have implications for policies surrounding the distribution of UGS and whether equitable access is provided to NYC residents, with implications for similar patterns that may exist in other cities.