  (Abridged) We have used the Rayner & Best (1989) smooth tests of
goodness-of-fit to study the Gaussianity of the Very Small Array (VSA) data.
Out of the 41 published VSA individual pointings dedicated to cosmological
observations, 37 are found to be consistent with Gaussianity, whereas four
pointings show deviations from Gaussianity. In two of them, these deviations
can be explained as residual systematic effects of a few visibility points
which, when corrected, have a negligible impact on the angular power spectrum.
The non-Gaussianity found in the other two (adjacent) pointings seems to be
associated to a local deviation of the power spectrum of these fields with
respect to the common power spectrum of the complete data set, at angular
scales of the third acoustic peak (l = 700-900). No evidence of residual
systematics is found in this case, and unsubstracted point sources are not a
plausible explanation either. If those visibilities are removed, a cosmological
analysis based on this new VSA power spectrum alone shows no differences in the
parameter constraints with respect to our published results, except for the
physical baryon density, which decreases by 10 percent. Finally, the method has
been also used to analyse the VSA observations in the Corona Borealis
supercluster region (Genova-Santos et al. 2005), which show a strong decrement
which cannot be explained as primordial CMB. Our method finds a clear deviation
(99.82%) with respect to Gaussianity in the second-order moment of the
distribution, and which can not be explained as systematic effects. A detailed
study shows that the non-Gaussianity is produced in scales of l~500, and that
this deviation is intrinsic to the data (in the sense that can not be explained
in terms of a Gaussian field with a different power spectrum).
