Local genetic correlation quantifies the genetic similarity of complex traits in specific genomic regions. However, accurate estimation of local genetic correlation remains challenging, due to linkage disequilibrium in local genomic regions and sample overlap across studies. We introduce SUPERGNOVA, a statistical framework to estimate local genetic correlations using summary statistics from genome-wide association studies. We demonstrate that SUPERGNOVA outperforms existing methods through simulations and analyses of 30 complex traits. In particular, we show that the positive yet paradoxical genetic correlation between autism spectrum disorder and cognitive performance could be explained by two etiologically distinct genetic signatures with bidirectional local genetic correlations.