  We present a theoretical study of the impact of an electric field combined
with a magnetic field on the rotational dynamics of open shell diatomic
molecules. Within the rigid rotor approximation, we solve the time-independent
Schr\"odinger equation including the fine-structure interactions and the
\Lambda-doubling effects. We consider three sets of molecule specific
parameters and several field regimes and investigate the interplay between the
different interactions identifying the dominant one. The possibility of
inducing couplings between the spin and rotational degrees of freedom is
demonstrated.
