The performance of decode-and-forward (DF) cooperative networks with relay selection is presented. Specifically, we derive closed-form expressions for symbol error probability (SEP), bit error rate (BER), and achievable spectral efficiency of DF relay selection system in independent but not identically distributed (i.n.i.d.) Rayleigh fading channels taking into account the incapability of decoding the received signals' cyclic redundancy code (CRC) at the relays. We also perform Monte-Carlo simulations to validate the analysis.