We define a statistic, called the matching statistic, for locating regions of the genome that exhibit excess similarity among cases when compared to controls. Such regions are reasonable candidates for harboring disease genes. We find the asymptotic distribution of the statistic while accounting for correlations among sampled individuals. We then use the Benjamini and Hochberg false discovery rate (FDR) method for multiple hypothesis testing to find regions of excess sharing. The p-values for each region involve estimated nuisance parameters. Under appropriate conditions, we show that the FDR method based on p-values and with estimated nuisance parameters asymptotically preserves the FDR property. Finally, we apply the method to a pilot study on schizophrenia.