This paper investigates quantization of the channel state information (CSI) in a cooperative cellular network. This CSI, delivered to some central node, is to be used to allocate resources in order to maximize the sum-rate in a multi-source network assisted by multiple relays. We start by deriving tight bounds on the performance loss due to quantization and then, through minimizing these bounds, we propose an efficient quantization and bit allocation technique. To this end, we present the bound on the overall performance loss as the sum of individual terms where each term represents the loss caused by the quantization of the CSI for an individual link. Then we show that each of these terms can be written as the product of two important components: the standard quantization error, and the link coefficient which is only a function of the large scale fading parameters. The quantization error is similar for all links and leads to the optimal quantization problem. Then using a simple bound on the quantization error, and also considering the link coefficients, we allocate bits to quantize each link. Further, we discuss the candidates in the network to play the role of the central node. A numerical example shows that the overall sum-rate (overall CSI demand), is significantly increased (decreased) through bit allocation.