Remote electronic voting is used in several countries for legally binding elections. Unlike academic voting protocols, these systems are not always documented and their security is rarely analysed rigorously. In this paper, we study a voting system that has been used for electing political representatives and in citizen-driven referenda in the Swiss canton of Neuchâtel. We design a detailed model of the protocol in ProVerif for both privacy and veri-fiability properties. Our analysis mostly confirms the security of the underlying protocol: we show that the Neuchâtel protocol guarantees ballot privacy, even against a corrupted server; it also ensures cast-as-intended and recorded-as-cast verifiability, even if the voter's device is compromised. To our knowledge, this is the first time a full-fledged automatic symbolic analysis of an e-voting system used for politically-binding elections has been realized.