Carsharing systems are adopting electric vehicles into their fleets and may therefore be able to provide not only transportation services to drivers/passengers but also energy services to the power grid through appropriate participation in electricity markets. This paper develops a queuing model of such carsharing platforms where cars may be deployed for transportation services at a given price, but also for grid services during transportation-idle periods through energy price arbitrage. The model provides a characterization of revenue from each of these two streams. The paper further finds optimal pricing and battery splitting to maximize revenue for the carsharing platform, via an analysis of the reward structure and an optimization algorithm. Platform revenue is assessed for various system parameters under optimal operation.