We present multilayer gene regulatory networks (GRNs) consisting of an intercellular layer and an intracellular layer. A network in an intercellular layer represents interactions between cells, and a network in an intracellular layer indicates interactions between genes. All the nodes of an intercellular network have identical random Boolean networks (RBNs) as intracellular GRNs. We introduce genetic perturbations (e.g., mutations) to the intracellular GRNs. Varying the properties of the intracellular GRNs from ordered, through critical, to chaotic regimes, we investigate how criticality of GRNs affects the robustness and evolvability of multilayer GRNs against the genetic perturbations. We found that the robust and evolvable multilayer GRNs were generated with the highest probability when intracellular GRNs were critical. Based on our findings, we conclude that the criticality of GRNs plays an important role in determining the robustness and evolvability of multilayer GRNs at a hierarchical level.