We study the influence of many-body interactions on the transport characteristics of a pair of quantum wires that are coupled to each other by means of a quantum dot. Under conditions where a local magnetic moment is formed in one of the wires, tunnel coupling to the other gives rise to an associated peak in its density of states, which can be detected directly in a conductance measurement. Our theory is therefore able to account for the key observations in the recent study of T. Morimoto et al. [Appl. Phys. Lett., ()]], and demonstrates that coupled quantum wires may be used as a system for the detection of local magnetic-moment formation.