Data processing on convolutional neural networks (CNNs) places a heavy burden on energy-constrained mobile platforms. This work optimizes energy on a mobile client by partitioning CNN computations between in situ processing on the client and offloaded computations in the cloud. A new analytical CNN energy model is formulated, capturing all major components of the in situ computation, for ASIC-based deep learning accelerators. The model is benchmarked against measured silicon data. The analytical framework is used to determine the optimal energy partition point between the client and the cloud at runtime. On standard CNN topologies, partitioned computation is demonstrated to provide significant energy savings on the client over fully cloud-based or fully in situ computation. For example, at 80 Mbps effective bit rate and 0.78 W transmission power, the optimal partition for AlexNet [SqueezeNet] saves up to 52.4% [73.4%] energy over a fully cloud-based computation, and 27.3% [28.8%] energy over a fully in situ computation.