Experimental data indicate that perceptual decision making involves integration of sensory evidence in certain cortical areas. Theoretical studies have proposed that the computation in neural decision circuits approximate statistically optimal decision procedures (e.g. sequential probability ratio test) that maximize reward rate in sequential choice tasks. However, these previous studies assumed that the sensory evidence was represented by continuous values from Gaussian distributions with the same variance across alternatives. In this paper we make a more realistic assumption that sensory evidence is represented in spike trains described by the Poisson processes, which naturally satisfy the mean-variance relationship observed in sensory neurons. We show that for such a representation, the neural circuits involving cortical integrators and basal ganglia can approximate the optimal decision procedures for two and multiple alternative choice tasks.