In this paper, we investigate the effects of channel estimation error at the receiver on the achievable rate of distributed space-time block coded transmission. We assume that multiple transmitters cooperate to send the signal to the receiver and derive lower and upper bounds on the mutual information of STBCs when the sub-channel gains and error variances between different transmitter-receiver links are unequal. We prove that the gap between these two bounds can not exceed a certain value at high transmit powers. We further prove that the gap between the mutual information bounds increases monotonically as a function of the input transmit power, and show that the gap is minimum if the receiver can estimate the channels pertaining to different transmitters with the same accuracy. We further derive closed-form expressions for the outage probability lower bound of distributed-STBCs (D-STBCs) with arbitrary number of transmitters. Numerical simulations are conducted to corroborate our analysis and quantify the effect of imperfect channel estimation.