This work investigates the end-to-end performance of randomized distributed space-time codes with complex Gaussian distribution, when employed in a wireless relay network. The relaying nodes are assumed to adopt a decode-and-forward strategy and transmissions are affected by small and large scale fading phenomena. Extremely tight, analytical approximations of the end-to-end symbol error probability and of the end-to-end outage probability are derived and successfully validated through Monte-Carlo simulation. For the high signal-to-noise ratio regime, a simple, closed-form expression for the symbol error probability is further provided.