A theoretical model to explain the phenomenon of spin crossover in the [MnL2]NO3 compound is elaborated. The model takes into account the low symmetry crystal field acting on the manganese ion and the cooperative long-range electron-deformational interaction facilitating the spin transition. The range of the crystal field parameters for which the low-lying part of the energy spectrum of an isolated MnIII ion consists of two orbitally non-degenerate levels with spins S=1 and 2 is determined. It is demonstrated that the S=1 state is the ground one in a narrow range of parameters. The ls-hs transition is considered as a cooperative phenomenon driven by the interaction of the electronic shells of the MnIII ions with the all-round full symmetric deformation that is extended over the crystal lattice via the acoustic phonon field. Quite good agreement has been obtained between the calculated and experimental values of the magnetic susceptibility and the effective magnetic moment.