  Phase relaxation of electrons transferring through an electromechanical
transistor is studied using the Aharonov-Bohm interferometer. With the approach
of quantum master equation, the phase properties of an electron are numerically
analyzed based on the interference fringes. Coherence of electron is partially
destroyed by its scattering on excited levels of the local nanomechanical
oscillator. Transmission amplitudes with respect to two adjacent mechanical
vibrational levels have a phase difference of $\pi$. The character of phase
shift by $\pi$ depends on the oscillator frequency only and is robust for the
wide range variance of the applied voltage, tunneling length and damping rate
of the mechanical oscillator.
