In this paper we develop a test for determining whether the observed sample path comes from a system with hysteresis perturbed by noise, or if it arises from a system governed by an ordinary differential equation with the same noise. A large sample size test is constructed, which is appropriate in many practical situations. Two models are considered as alternatives to the hysteresis model. An asymptotic expression for the cutoff point of the test is found using a version of the central limit theorem.