This paper presents a privacy-preserving event detection scheme based on measurements made by a network of sensors. A diameter-like decision statistic made up of the marginal types of the measurements observed by the sensors is employed. The proposed detection scheme can achieve the best type-I error exponent as the type-II error rate is required to be negligible. Detection performance with finite-length observations is also demonstrated through a simulation example of spectrum sensing. Privacy protection is achieved by obfuscating the sensors' marginal types with random zero-modulo-sum numbers that are generated and distributed via the exchange of encrypted messages among the sensors. The privacy-preserving performance against "honest but curious" adversaries, including colluding sensors, the fusion center, and external eavesdroppers, is analyzed through a series of cryptographic games. It is shown that the probability that any probabilistic polynomial time adversary successfully estimates the sensors' measured types cannot be much better than independent guessing, when there are at least two non-colluding sensors.