We consider a multi-relay system where the best single relay is selected to assist transmissions. We study the performance bound of the system in the finite blocklength regime. On the one hand, we extend Polyanskiy's finite blocklength model of a single-hop scenario to the considered relaying system and derive the corresponding achievable throughput. On the other hand, by employing a practical coding scheme, namely polar codes, a finite blocklength performance bound attainable by a low-complexity coding scheme is provided. Through simulation and numerical investigations, we show the appropriateness of the proposed bounds. Moreover, we evaluate both the achievable performance with finite blocklengths and the performance of polar codes in the best single relay scenario in comparison to direct transmission.