We study the statistics of photon emission from three-level single molecule systems. The generating function method [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] is used to calculate steady state absorption line shapes and Mandel's Q parameter as a function of excitation frequency, as well as the time dependence associated with approach to the steady state. The line shape calculations confirm known results derived via other methods, while the Q parameter results display complex frequency dependences not amenable to simple interpretation. This study confirms the applicability of the generating function formalism to multilevel quantum systems, including the proper modeling of quantum coherence effects.