With the urbanization and development of infrastructure, the community search over road networks has become increasingly important in many real applications such as urban/city planning, social study on local communities, and community recommendations by real estate agencies. In this paper, we propose a novel problem, namely top-k community similarity search (Top-kCS2) over road networks, which efficiently and effectively obtains k spatial communities that are the most similar to a given query community in road-network graphs. In order to efficiently and effectively tackle the Top-kCS2 problem, in this paper, we will design an effective similarity measure between spatial communities, and propose a framework for retrieving Top-kCS2 query answers, which integrates offline pre-processing and online computation phases. Moreover, we also consider a variant, namely continuous top-k community similarity search (CTop-kCS2), where the query community continuously moves along a query line segment. We develop an efficient algorithm to split query line segments into intervals, incrementally obtain similar candidate communities for each interval and define actual CTop-kCS2 query answers. Extensive experiments have been conducted on real and synthetic data sets to confirm the efficiency and effectiveness of our proposed Top-kCS2 and CTop-kCS2 approaches under various parameter setting