  We report on the crystallographic information such as lattice parameters,
atomic positions, bond lengths and angles, and local crystalline distortion
size and mode of single-crystal YCrO$_3$ compound by a high-resolution
synchrotron X-ray diffraction study. The data was collected at 120 K (below
$T_\textrm{N} \sim$ 141.5 K), 300 K (within [$T_\textrm{N}$, $T_\textrm{C}$]),
and 500 K (above $T_\textrm{C} \sim$ 473 K). Taking advantages of high
intensity and brilliance of synchrotron X-rays, we are able to refine collected
patterns with the noncentrosymmetric monoclinic structural model ($P12_11$, No.
4) that was proposed previously but detailed structural parameters have not
determined yet. Meanwhile, we calculated patterns with the centrosymmetric
orthorhombic space group (\emph{Pmnb}, No. 62) for a controlled study. Lattice
constants \emph{a}, \emph{b}, and \emph{c} as well as unit-cell volume almost
increase linearly upon warming. We observed more dispersive distributions of
bond length and angle and local distortion strength with the $P12_11$ space
group. This indicates that (i) The local distortion mode of Cr2O$_6$ at 120 K
correlates the formation of the canted antiferromagnetic order by Cr1-Cr2 spin
interactions mainly through intermediate of O3 and O4 ions. (ii) The
strain-balanced Cr1-O3(O4) and Cr2-O5(O5) bonds as well as the local distortion
modes of Cr1O$_6$ and Cr2O$_6$ octohedra at 300 K may be a microscopic origin
of the previously-reported dielectric anomaly. Our study demonstrates that
local crystalline distortion is a key factor for the formation of ferroelectric
order and provides a complete set of crystallography for a full understanding
of the interesting magnetic and quasi-ferroelectric properties of YCrO$_3$
compound.
