Such tests are typically formulated for isolated systems — an assumption that breaks down in any experimental implementation. In this work, we extend the protocol to a harmonic oscillator coupled to standard models of dissipation: thermal relaxation, pure dephasing, and the Caldeira–Leggett model. Working within the Moyal–Wigner phase-space formalism, we show that dissipation generically shifts the classical bound of the witness, and we derive explicit, environment-dependent thresholds on the dissipation strength below which the witness remains a faithful certificate of nonclassicality. Our results establish the regime of validity of dynamics-based nonclassicality tests under realistic noise conditions.