In this paper, we study the energy-efficient user access control (UAC) based on resource allocation (RA) in heterogeneous cellular networks (HCNs) with the required downlink data rate under non-ideal power amplifiers (PAs) and circuit power. It is proved that the energy consumption minimization is achieved when the typical user accesses only one base station (BS), while the other BSs remain in idle mode on the transmission resource allocated to this user. For this purpose, we reformulate the original non-convex optimization problem into a series of convex optimization problems where, in each case, the transmit power and duration of the accessed BS are determined. Then, the BS with the minimal energy consumption is selected for transmission. Considering the approximate situation, it is showed that the optimal transmit duration of the accessed BS can be estimated in closed form. The benefits of our proposed UAC and RA schemes are validated using numerical simulations, which also characterize the effect that non-ideal PAs have on the total energy consumption of different transmission schemes.