  In the recent work [Phys. Rev. D 91, 111702(R) (2015)], C. Hill concludes
that the axion electromagnetic anomaly induces an oscillating electron electric
dipole moment of frequency $m_a$ and strength $\sim 10^{-32}~e$ cm, in the
limit $v/c \to 0$ for the axion field. Here, we demonstrate that a proper
treatment of this problem in the lowest order yields $\textit{no}$ electric
dipole moment of the electron in the same limit. Instead, oscillating electric
dipole moments of atoms and molecules are produced by different mechanisms.
