  The purpose of this note is to prove global-in-time smoothing effects for the
Schr\"odinger equation with potentials exhibiting critical singularity. A
typical example of admissible potentials is the inverse-square potential
$a|x|^{-2}$ with $a>-(n-2)^2/4$. This particularly gives an affirmative answer
to a question raised by Bui-D'Ancona-Duong-Li-Ly [4]. The proof employs a
uniform resolvent estimate proved by Barcel\'o-Vega-Zubeldia [1] and an
abstract perturbation method by Bouclet-Mizutani [3].
