External electric fields can halt the rotation of polar molecules and produce pendular states in which the molecular dipole μ is confined to librate over a limited angular range about the space-fixed direction of the external field. The pendular eigenfunctions are hybrids of field-free rotor states, (J,K,M) with indefinite (forK≠ 0) or alternating (forK= 0) parities; this renders the parity of the hybrid wavefunctions indefinite for any values of the good quantum numbersKorM. As a result, the parity selection rule for the matrix elements of tensor operators in the pendular basis, notably the electric dipole moment, is lifted. We give the expectation values of the space-fixed dipole moment operator and of the orientation cosine of the figure axis and illustrate the lifting with field strength of the parity selection rule for prototype hybrid states of polar molecules. The symmetry properties of the pendular Hamiltonian are used to sort the eigenstates according to the sign of the product ofK, M, and μ.