Point process data is increasingly occurring in a wide range of applications including social media. But basic problems such as classifying point processes have not been addressed. Here we study the misclassification error of a point process Bayes rule/likelihood ratio classification rule in a binary classification problem. We first develop the Bhattacharya bound for the error rate for the time-varying Poisson. We then derive a tight computable bound on the Bhattacharya bound for the renewal process. We then develop fast methods for computing these bounds. We study the accuracy of the bounds with some comparative simulations.