In recent years, a large number of time series microbial community data has been produced in molecular biological studies, especially in metagenomics. Among the statistical methods for time series, local similarity analysis is used in a wide range of environments to capture potential local and time-shifted associations that cannot be distinguished by traditional correlation analysis. Initially, the permutation test is popularly applied to obtain the statistical significance of local similarity analysis. More recently, a theoretical method has also been developed to achieve this aim. However, all these methods require the assumption that the time series are independent and identically distributed. In this paper, we propose a new approach based on moving block bootstrap to approximate the statistical significance of local similarity scores for dependent time series. Simulations show that our method can control the type I error rate reasonably, while theoretical approximation and the permutation test perform less well. Finally, our method is applied to human and marine microbial community datasets, indicating that it can identify potential relationship among operational taxonomic units (OTUs) and significantly decrease the rate of false positives.