The nonlinear behavior of automotive powertrains is mainly due to the presence of backlash between engaging components. In particular, during tip-in or tip-out maneuvers, backlash allows the generation of impacts that negatively affect the vehicle NVH performance. Due to the faster response of electric machine with respect to conventional internal combustion engines, this problem is even more critical for electric vehicles. In order to employ numerical optimal control methods for backlash compensation, the powertrain torsional system states have to be known. In this paper, an electric powertrain is modeled as a two-mass oscillator with lumped backlash. This model estimates the system states when in non-contact mode while a Kalman filter that relies only on commonly available speed measurements (motor and wheels) is active in the contact phase. The powertrain model is validated using experimental data collected during vehicle testing and the online estimated half-shaft torque is shown. In addition, simulations are performed to illustrate that the system states can be properly determined with the proposed estimator.