Under the carbon cap-and-trade policy, a co-opetitive supply chain system composed of an original equipment manufacturer (OEM) with production outsourcing and a competing contract manufacturer (CM) is constructed. Considering the spillover effect, the issue of the choice of supply chain emission reduction investment strategies is studied by comparing four scenarios: no emission reduction investment, emission reduction investment by a CM, emission reduction investment by an OEM, and joint emission reduction investment. The research findings are as follows: Firstly, compared with no investment, the CM can always benefit from investment. In most cases, the CM chooses joint investment. However, when competition is dominant, the CM will choose to invest alone. For the OEM, free-riding is not always profitable, and joint investment can significantly improve its benefits. Secondly, when cooperation dominates in the co-opetitive relationship or the competition is relatively weak, joint investment is the equilibrium strategy for both the CM and the OEM. Thirdly, the carbon trading price and the spillover coefficient will affect the tendency of enterprises between competition and cooperation, regulate the co-opetitive relationship among enterprises, and further influence the decision-making behaviors of supply chain enterprises. Finally, under normal circumstances, supply chain emission reduction investment can achieve better environmental performance, but when the initial carbon emissions per unit of product are very large, the "emission reduction effort dilemma" will occur.