  We present $^{127}$I nuclear quadrupole resonance spectra and nuclear
relaxation of $\alpha$-(BEDT-TTF)$_2$I$_3$ that undergoes a charge-ordering
transition. Only one of the two I$_3$ anion sites shows a significant
differentiation in the electric field gradients across the first-order
transition. The charge modulation only in the BEDT-TTF layers can not
reproduce; instead, an anion-donor interaction accompanied by hydrogen bonding
is necessary. The dominating source for the nuclear relaxation is the local
libration of the I$_3$ anions, but an anomalous peak is detected just below the
transition, as observed by $^{13}$C NMR.
