  We investigate single-particle energy spectra of the hydroxyl free radical
(OH) in the lowest electronic and rovibrational level under combined static
electric and magnetic fields, as an example of heteronuclear polar diatomic
molecules. In addition to the fine-structure interactions, the hyperfine
interactions and centrifugal distortion effects are taken into account to yield
the zero-field spectrum of the lowest ${}^2\Pi_{3/2}$ manifold to an accuracy
of less than 2 kHz. We also examine level crossings and repulsions in the
hyperfine structure induced by applied electric and magnetic fields. Compared
to previous work, we found more than 10 percent reduction of the magnetic
fields at level repulsions in the Zeeman spectrum subjected to a perpendicular
electric field. It is important to take into account hyperfine structure when
we investigate physics of OH molecules at micro-Kelvin temperatures and below.
