In this work, we propose a novel framework for distributed detection by resorting to the Random Distortion Testing with linear measurements (RDTlm) approach. The goal is to collaboratively detect a signal, with unknown distribution embedded in noise, with the help of multiple sensors distributed spatially in the Region of Interest (RoI). The sensors observe the phenomenon and forward a compressed summary of the observations to a Fusion Center (FC). The FC then employs RDTlm to perform the hypothesis test. In contrast to classical likelihood ratio based approaches that cannot be employed in case of imprecise knowledge of the signal distributions, framing the problem within the RDTlm framework leads to performance guarantees, irrespective of the signal distributions under each hypothesis and without the need to estimate the unknown distributions. Moreover, we show the equivalence between the proposed distributed approach where a compressed summary is forwarded by the sensors and the centralized approach where the sensors forward raw observations to the FC.