  [Abridged.] It is conceivable that no single statistical estimator can be
sensitive to all forms and levels of non-Gaussianity that may be present in
observed CMB data. In recent works a statistical procedure based upon the
calculation of the skewness and kurtosis of the patches of CMB sky-sphere has
been proposed and used to find out significant large-angle deviation from
Gaussianity in the foreground-reduced WMAP maps. Here we address the question
as to how the analysis of Gaussianity of WMAP maps is modified if the
foreground-cleaned Planck maps are used, therefore extending and complementing
the previous analyses in several regards. We carry out a new analysis of
Gaussianity with the available nearly full-sky foreground-cleaned Planck maps.
As the foregrounds are cleaned through different component separation
procedures, each of the resulting Planck maps is then tested for Gaussianity.
We determine quantitatively the effects for Gaussianity of masking the
foreground-cleaned Planck maps with the INPMASK, VALMASK, and U73 Planck masks.
We show that although the foreground-cleaned Planck maps present significant
deviation from Gaussianity of different degrees when the less severe INPMASK
and VALMASK are used, they become consistent with Gaussianity as detected by
our indicator $S$ when masked with the union U73 mask. A slightly smaller
consistency with Gaussianity is found when the $K$ indicator is employed, which
seems to be associated with large-angle anomalies reported by the Planck team.
Finally, we examine the robustness of the Gaussianity analyses with respect to
the noise pixel's as given by the Planck team, and show that no appreciable
changes arise when is incorporated into the maps. The results of our analyses
provide important information about the suitability of the foreground-cleaned
Planck maps as Gaussian reconstructions of the CMB sky.
