The problem of node-centric, or local, community detection in information networks refers to the identification of a community for a given input node, having limited information about the network topology. Existing methods for solving this problem, however, are not conceived to work on complex networks. In this paper, we propose a novel framework for local community detection based on the multilayer network model. Our approach relies on the maximization of the ratio between the community internal connection density and the external connection density , according to multilayer similarity-based community relations. We also define a biasing scheme that allows the discovery of local communities characterized by different degrees of layer-coverage diversification. Experimental evaluation conducted on real-world multilayer networks has shown the significance of our approach.