  We classify all the first-order vertices of gravity consistently coupled to a
system of 2-form gauge fields by computing the local BRST cohomology H(s|d) in
ghost number 0 and form degree n. The consistent deformations are at most
linear in the undifferentiated two-form, confirming the previous results of [1]
that geometrical theories constructed from a nonsymmetric gravity theory are
physically inconsistent or trivial. No assumption is made here on the degree of
homogeneity in the derivatives nor on the form of the gravity action.
