Starting with the most general dimension six beyond the standard model Hamiltonian we derive the four fold angular distributions for $B \to D \pi \ell \bar{\nu}$ mode, where the $D\pi$ final state arises from a vector $D^*$ or a tensor meson $D_2^*$ onshell decay. Distinguishable features in the angular distributions of these two modes are explored. Plenty of observables are constructed with which the experimental information would help to disentangle the dynamical origin of the observed deviations in $b \to c \tau \bar{\nu}$ transition.