  In this paper, we reassess a particular $R^{2}$-type gravity action in D
dimensions, recently studied by Nakasone and Oda, taking now torsion effects
into account. Considering that the vielbein and the spin connection carry
independent propagating degrees of freedom, we conclude that ghosts and
tachyons are absent only if torsion is non-propagating, and we also conclude
that there is no room for massive gravitons. To include these excitations, we
understand how to enlarge Nakasone-Oda's model by means of explicit torsion
terms in the action and we discuss the unitarity of the enlarged model for
arbitrary dimensions.
