In this paper, we analyse the call completion probability in a two-tier heterogeneous network (HetNet), where all base stations (BSs) in each tier are powered solely by energy harvesting. Since energy harvesting BSs may need to be kept OFF and allowed to recharge, users connected to a BS that turns OFF need to be served by neighboring BSs that are ON. This hand-off of a call can impact the call performance from a users point of view. We formulate the call completion probability for HetNets by adapting the definition from traditional cellular networks. Adopting a realistic BS energy consumption model and using tools from stochastic geometry, we derive very tight upper and lower bounds on the call completion probability in the presence of Rayleigh fading, interference and energy harvesting BSs. We examine the impact of the system parameters on the completion probability. The results show that the macro BS energy harvesting parameters have the dominant impact on the call completion probability. In particular, the call completion probability is an increasing function of the macro BS battery capacity and the minimum energy level at which macro BS switches back ON. However, it is an increasing function of the macro BS energy harvesting rate only when the macro BS battery capacity and the minimum energy level at which macro BS switches back ON are large. The results can be used in network planning to ensure certain quality-of-service (QoS) to users in terms of call completion probability.