Cloud radio access network (CRAN) architecture is proposed to save energy, facilitate coordination between radio units, and achieve scalable solutions to improve radio network's performance. However, stringent delay and bandwidth constraints are incurred by fronthaul in CRAN [the network segment connecting RUs and digital units (DUs)]. Therefore, we propose a hybrid cloud radio access network architecture, where a DU's functionalities can be virtualized and split at several conceivable points. Each split option results in two-level deployment of the processing functions (central site level and remote site level) connected by a transport network, called midhaul. We study the interplay of energy efficiency and midhaul bandwidth consumption under optimal processing allocation. We jointly minimize the power and midhaul bandwidth consumption in H-CRAN, while satisfying network constraints, i.e., processing and midhaul bandwidth capacity. We enable power saving functionalities by shutting down different network components. The proposed model is formulated as a constraint programming problem. The proposed solution shows that 42 percentile of midhaul bandwidth savings can be achieved compared to the fully centralized CRAN; and 35 percentile of power consumption saving can be achieved compared to the case where all the network functions are distributed at the edge.