In this paper, a distributed solar hybrid combined cooling, heating, and power (CCHP) system is constructed by installing photovoltaic/thermal (PV/T) panels in the CCHP (PV/T-CCHP) system. A bi-level optimization model is established to obtain the optimal sizing of the equipment in the PV/T-CCHP. The upper-level optimization model is formulated as a multi-objective optimization problem, which considers the economic, energy, and environmental performance of the PV/T-CCHP system compared with the conventional separated production system. The equipment sizing results obtained by the upper-level optimization model can achieve the trading off in terms of cost, primary energy consumption, and carbon emission reduction. The lower-level optimization model, which is formulated as a mixed-integer linear programming, determines the operating strategy of the PV/T-CCHP system. Non-dominated sorting genetic algorithm-II is employed to solve the upper-level optimization model. The final optimal sizing results are obtained from the Pareto solution set leveraging fuzzy decision theory. The optimal sizing results demonstrate that PV/T-CCHP saves 5.82% in annual total cost, 22.63% in annual primary energy, and 37.51% in annual carbon emissions reduction, which verifies the effectiveness of the proposed optimization model. In addition, the impacts of solar energy and energy storage equipment on the system performance are quantitatively evaluated.