As the International Maritime Organization increasingly imposes stringent requirements on ship operational carbon intensity, a detailed analysis of the energy consumption structure of shipboard energy systems is essential. In contrast to the integral assessment applied in the calculation of the Carbon Intensity Indicator (CII), particular interest lies in the quantitative evaluation of the contribution of individual auxiliary energy systems that impose an additional load on the ship’s power plant and, consequently, contribute to operational CO₂ emissions. For LNG carriers, this issue is particularly important due to the implementation of boil-off gas (BOG) reliquefaction systems, which return vaporized LNG to the liquid phase and maintain the required cargo storage conditions. The impact of these systems on the vessel’s carbon-intensity indicators requires a quantitative assessment. The considered BOG reliquefaction plant operates based on an indirect liquefaction process employing a mixed refrigerant cycle. The thermodynamic analysis was carried out using an entropy-based approach, with data from sea trials, enabling the determination of the distribution of entropy generation and the integral performance characteristics of the process. It was found that the major share of entropy generation is concentrated in the BOG/LNG circuit, with the dominant contribution associated with the operation of the cargo compressor. In the mixed refrigerant circuit, irreversibilities are mainly attributed to compression in the MR compressor and throttling in the expansion valve. The cycle thermodynamic effectiveness is 0.82; however, this value should be regarded as an upper estimate due to the neglect of hydraulic losses, heat ingress, and auxiliary energy consumption. Based on the obtained thermodynamic characteristics, the analysis was extended to the evaluation of environmental performance indicators. The BOG handling system consumes 588 kW, including 283 kW in the cargo circuit and 304 kW in the reliquefaction plant circuit. CO₂ emissions associated with the operation of the BOG handling system amount to 5.46 t per day, which, when expressed in terms of carbon intensity, corresponds to 0.22 g CO₂/(t·nm) and a contribution of 1% to the overall CII of the LNG carrier, indicating the limited effect of this system on the vessel’s integrated carbon intensity. The obtained results provide a basis for the quantitative assessment of the BOG reliquefaction plant's contribution.