  We examine the impact of the combination of a static electric field and a non
resonant linearly polarized laser field on an asymmetric top molecule. Within
the rigid rotor approximation, we analyze the symmetries of the Hamiltonian for
all possible field configurations. For each irreducible representation, the
Schr\"odinger equation is solved by a basis set expansion in terms of a linear
combination of Wigner functions respecting the corresponding symmetries, which
allows us to distinguish avoided crossings from genuine ones. Using the
fluorobenzene and pyridazine molecules as prototypes, the rotational spectra
and properties are analyzed for experimentally accessible static field
strengths and laser intensities. Results for energy shifts, orientation,
alignment and hybridization of the angular motion are presented as the field
parameters are varied. We demonstrate that a proper selection of the fields
gives rise to a constrained rotational motion in the three Euler angles, the
wave function being oriented along the electrostatic field direction, and
aligned in the other two angles.
