In this paper, we investigate time-domain equalization for distributed space-time codes in a relay-assisted transmission scenario over frequency-selective fading channels. Specifically, we consider the so-called time-reversal space-time block coding (TR-STBC) technique which has been of particular interest with its low computational complexity. We assume the special case of a single-relay where the source-to-relay (S → R), relay-to-destination (R → D), and source-to-destination (S → D) links experience possibly different channel delay spreads. Under the assumption of perfect power control for the relay terminal and high signal-to-noise ratio for the underlying links, our performance analysis demonstrates that distributed TR-STBC is able to achieve a maximum diversity order of min (L1, L3) + L2 + 2 where L1, L2, and L3 are the channel memory lengths for S → R, S → D, and R → D links, respectively. This illustrates that the smaller of the multipath diversity orders experienced in S → R and R → D links becomes the performance bottleneck for the relaying path. An extensive Monte Carlo simulation study is presented to corroborate the analytical results and to provide detailed performance comparisons with competing schemes.