In this paper, we derive a maximum-likelihood (ML) decoder for the demodulate-and-forward (DF) based cooperative communication system using Alamouti space-time block code (STBC) in a distributed manner. We also propose a sub-optimal low complexity piece-wise linear (PL) decoder of the distributed Alamouti code in a DF cooperative system in which one relay out of two relays is in outage. The proposed PL decoder does not lead to any significant performance degradation and performs very close to the proposed ML decoder. Moreover, the proposed ML decoder of the DF cooperative system significantly outperforms an amplify-and-forward (AF) based cooperative system when both systems use the same data rate and distributed Alamouti STBC.