To deal with the growing phenomenon of electromigration (EM), power grid current integrity verification becomes indispensable to designing reliable power delivery networks (PDNs). Unlike previous works that focus on vectorless voltage integrity verification of power grids, in this work, for the first time we present a scalable vectorless power grid current integrity verification framework. By taking advantage of multilevel power grid verifications, large-scale power grid current integrity verification tasks can be achieved in a very efficient way. Additionally, a novel EM-aware geometric power grid reduction method is proposed to well preserve the similar geometric and electrical properties of the original grid on the coarse-level power gri...