The Patient Transportation Problem (PTP) aims to bring patients to health centers and to take them back home once the care has been delivered. All the requests are known beforehand and a schedule is built the day before its use. It is a variant of the well-known Dial-a-Ride Problem (DARP) but it has nevertheless some characteristics that complicate the decision process. Three levels of decisions are considered: selecting which requests to service, assigning vehicles to requests and routing properly the vehicles. In this paper, we propose a Constraint Programming approach to solve the Patient Transportation Problem. The model is designed to be flexible enough to accommodate new constraints and objective functions. Furthermore, we introduce a generic search strategy to maximize efficiently the number of selected requests. Our results show that the model can solve real life instances and outperforms greedy strategies typically performed by human schedulers.