We use a field theory approach to study the effects of permanent dipoles on interpenetration and free energy changes as a function of distance between two identical planar polymer brushes. Melts (i.e., solvent free) and solvated brushes made up of polymers grafted on nonadsorbing substrates are studied. In particular, the weak coupling limit of the dipolar interactions is considered, which leads to concentration-dependent pairwise interactions, and the effects of orientational order are neglected. It is predicted that a gradual increase in the dipole moment of the polymer segments can lead to attractive interactions 'between the brushes at intermediate separation distances. Because classical theory of polymer brushes based on the strong stretching limit (SSL) and the standard self consistent field theory (SCFT) simulations using the Flory's chi parameter always predicts repulsive interactions at all separations, our work highlights the importance of dipolar interactions in tailoring and accurately predicting forces between polar polymeric interfaces in contact with each other.