This paper concerns rotational energy levels and line intensities for electronic, vibrational, and microwave transitions in an open-shell complex consisting of an open-shell diatomic molecule and a closed-shell partner. The electronic state of the open-shell diatomic fragment is a 2Sϩ1 ⌺ state, where S Ն 1 2 , the close-shell partner could be a rare gas atom or a diatomic molecule or a planar polyatomic molecule. We are considering a near-rigid rotor model for a nonlinear complex, taking into account thoroughly all effects of the electron spin and the quartic centrifugal distortion correction terms. The total Hamiltonian is expressed as HϭH rot ϩH sr ϩH ss ϩH cd ϩH srcd ϩH sscd . We have derived all the nonvanishing matrix elements of the Hamiltonian operators in the molecular basis set. The rotational energy levels are calculated by numerical diagonalization of the total Hamiltonian matrix for each J value. The nonvanishing matrix elements of the electric dipole moment operator are derived in the molecular basis set for electronic, vibrational, and microwave transitions within the complex. Expectation values of the quantum numbers and of the parities of the rotational states are derived in the molecular basis set. Relative intensities of the allowed rotational transitions, expectation values of the quantum numbers and the parities are calculated numerically in the space of the eigenvectors obtained from diagonalization of the Hamiltonian matrix. The formalism and the computer program of this paper are considered as extensions to our previous work [