We report muon spin relaxation measurements results on UCu1.5Sn2, which crystallizes in the CaBe2Ge2-type structure. Our analysis is consistent with collinear antiferromagnetic order that occurs below 108K, in agreement with previous reports. The Brillouin-like behavior of the temperature dependence of the magnetic response is consistent with localized 5f moments. The phase transition at TN is unusual. Critical slowing down for the paramagnetic U spin fluctuations is absent, a behavior usually observed in first-order transitions. In contrast, the temperature dependence of the local field generated by the U spins is a typical second-order feature.