Car sharing services promise "green" transportation systems. Two vehicle technologies offer marketable, sustainable sharing: autonomous vehicles (AVs) eliminate customer requirements for car pick-up and return, and battery electric vehicles entail zero emissions. Designing an autonomous electric vehicle (AEV) fleet must account for the relationships among fleet operations, charging station (CS) operations, electric powertrain performance, and consumer demand. This paper presents a system design optimization framework integrating four subsystem problems: fleet size and assignment schedule; number and locations of charging stations; vehicle powertrain requirements; and service fees. We also compare an AEV service and autonomous vehicle (AV) service with gasoline engines. A case study for an autonomous fleet operating in Ann Arbor, MI, is used to examine AEV and AV sharing systems profitability and feasibility for a variety of market scenarios. The results provide practical insights for service system decision makers.