Using complex modal superposition, the Randomdec signatures are investigated for the random responses of a linear time-invariant multiple-degree-of-freedom system with non-proportional damping. The input is assumed to be Gaussian white noise with zero mean. Through rigorous mathematical derivation and numerical simulations, this paper presents three properties of the Randomdec signatures to supplement the mathematical basis for the random decrement technique so that the Randomdec signatures will not be misused in the further system identification. First, the estimations of auto- and cross-Randomdec signatures are proved to be unbiased, and the variances of the estimated auto- and cross-Randomdec signatures are proved to be proportional to the variances of the raw data and inversely proportional to the number of records used. Second, under certain circumstances, the Randomdec displacement and velocity signatures are equivalent to the corresponding free decay responses of the system while the Randomdec acceleration signature is never equivalent to the free decay signals. Third, the singular behaviour of Randomdec acceleration signatures depends on the singularities of input correlation functions as well as the mass matrix of the system under consideration.