This paper presents a decomposed co-design optimization framework for an electric vehicle powertrain equipped with a Continuously Variable Transmission (CVT). We jointly design the sizes of the powertrain components and the energy management strategy, considering the design and the dynamics of the transmission. Specifically, we divide the resulting nonlinear optimization problem into separate hierarchical optimization subproblems leveraging the concept of Analytical Target Cascading (ATC). Furthermore, we compare the proposed decomposition-based strategy with a centralized approach, in which we solve the same problem, and show that the method presented in this paper can be a potential alternative to a centralized optimization formulation fo...