Distributed space-time block coding (Dis-STBC) achieves diversity through cooperative transmission among geographically dispersed nodes. In this paper, we present a power-efficient relay-selection strategy for decentralized Dis-STBC in a selective decode-and-forward cooperative network. In particular, for a two-stage network, each decoded node broadcasts a small amount of information with limited power. This node then utilizes its own and its neighbors' information to decide whether or not to act as a relay for the source information. In this way, only part of the decoded set will act as relays. Further, by applying the idea of this relay-selection strategy to each relaying hop in a multihop network, a power-efficient hop-by-hop routing strategy is formulated. The outage analyses and simulations are presented to illustrate the advantage of these strategies.