Motivated by our recent finding that the singlet-triplet bands of selenoformaldehyde involve an upper state with large zero field splittings, we have extended the theory and written a program for predicting and fitting such rotationally resolved spectra. Triplet state matrix elements for a case ͑A͒ basis have been developed, including corrections for centrifugal and spin-centrifugal distortion. The full Hamiltonian matrix has been symmetry adapted, simplifying the problem to four individual matrices of approximately equal size for molecules of orthorhombic symmetry. Diagonalization of these matrices yields triplet state energies that are in agreement with previous treatments using a basis in which the spin splittings are small relative to the rotational intervals. Methods have been developed for sorting the eigenvalues and assigning quantum labels regardless of the magnitude of the spin splittings. The calculation of the relative intensities of the rotational lines within a band has been programmed using transition moment matrix elements from the literature. The selection rules for various upper state symmetries have been developed in a form useful for the analysis of spectra. Band contour predictions of spectra for various coupling cases have been presented.