The electron spin resonance (ESR) measurements made on the highly conducting Langmuir-Blodgett (LB) films of a charge-transfer complex of bis(ethylenedioxy)tetrathiafulvalene (BO) and decyltetracyanoquinodimethane (C(10)TCNQ), mixed with icosanoic acid, revealed microscopically the metallic nature of the system in a wide temperature range. Further, an anomalous increase in the ESR linewidth was detected around 140 K. To elucidate the origin of this anomaly, in situ ESR experiments upon annealing at low temperatures have been performed. The temperature dependence of the infrared spectrum has been also measured. The obtained results indicate a possible low-temperature phase transition of the present conducting LB system.