  In this paper we generalize our previous results on spin connection for the
linear scalar cosmological perturbation in $f(T)$ theory to wider class of
theories which includes a scalar field $\Phi$ non-minimally coupled to torsion,
and allows $\Phi$-dependence of the function $f$. The case of $f_{TT}=0$, with
a scalar field non-minimally coupled to torsion needs a special treatment. In
both considered cases we derive self-consistent equations of motion for
cosmological perturbation using a solution for non-trivial spin connection.
