This work studies the optimization of rate-splitting multiple access (RSMA) transmission technique for a cloud radio access network (C-RAN) downlink system. Main idea of RSMA is to split the message for each user equipment (UE) to private and common messages and perform superposition coding at transmitters so as to enable flexible decoding at receivers. It is challenging to implement ideal RSMA scheme particularly when there are many UEs, since the number of common signals exponentially increases with the number of UEs. An efficient RSMA scheme is hence proposed that uses a linearly increasing number of common signals whose decoding UEs are selected using hierarchical clustering. Via numerical results, we show the performance gains of the proposed RSMA scheme over conventional space-division multiple access (SDMA) and nonorthogonal multiple access (NOMA) schemes as well as over a conventional RSMA scheme that uses a single common signal.