  We use the \delta N formalism to study the trispectrum T_\zeta of the
primordial curvature perturbation \zeta when the latter is generated by vector
field perturbations, considering the tree-level and one-loop contributions. The
order of magnitude of the level of non-gaussianity in the trispectrum,
\tau_{NL}, is calculated in this scenario and related to the order of magnitude
of the level of non-gaussianity in the bispectrum, f_{NL}, and the level of
statistical anisotropy in the power spectrum, g_\zeta. Such consistency
relations will put under test this scenario against future observations.
Comparison with the expected observational bound on \tau_{NL} from WMAP, for
generic inflationary models, is done.
