In a previous paper [arXiv:2106.04659], the authors proved the existence of local-in-time weak solutions to a model of superfluidity. The system of governing equations was derived by Pitaevskii in 1959 and couples the nonlinear Schrödinger equation (NLS) and the Navier-Stokes equations (NSE). In this article, we prove two uniqueness theorems for these weak solutions. One of them is the classical weak-strong uniqueness based on a relative entropy method. The other result trades some regularity of the stronger solution for smallness of data and short time/low energy.