With the reduction of sequencing costs and the pervasiveness of computing devices, genomic data collection is continually growing. However, data collection is highly fragmented and the data is still siloed across different repositories. Analyzing all of this data would be transformative for genomics research. However, the data is sensitive, and therefore cannot be easily centralized. Furthermore, there may be correlations in the data, which if not detected, can impact the analysis. In this paper, we take the first step towards identifying correlated records across multiple data repositories in a privacy-preserving manner. The proposed framework, based on random shuffling, synthetic record generation, and local differential privacy, allows a trade-off of accuracy and computational efficiency. An extensive evaluation on real genomic data from the OpenSNP dataset shows that the proposed solution is efficient and effective.