We address the problem of studying the number of excitatory stimuli producing a spike for a Stein-type stochastic model which includes a multiplicative state-dependent effect. Some results on the probability distribution of the number M of excitatory stimuli triggering a spike are obtained. We also evaluate the distribution of M conditional on the firing time, and disclose some properties of its mode. Finally, some results on the probability generating function of the conditional distribution are given.