Cloud radio access networks (C-RAN) and millimeter wave (mmwave) based remote radio heads (RRHs) have been proposed in 5G. Further, dual connectivity (DC) has been introduced in cellular networks to increase the per-user throughput of the system. The implementation of DC requires user's information to be shared and processed for all the participating RRHs. In this work, we consider DC in C-RAN with mmwave based fronthaul between the virtualized base band unit (BBU) pool and the RRHs. Given a generalized \alpha-fair scheduler, the resource allocation problem for the mmwave based fronthaul is formulated for a DC system. The optimal time fraction that the virtualized BBU pool should serves each RRH is analytically derived. Further, the association of DC is numerically solved with this fronthaul resource allocation. Numerical results are presented that indicate that the proposed solution outperforms the existing benchmark in terms of the user throughput for a marginal increase in the required fronthaul capacity. © 2019 IEEE.