A system of two harmonic oscillators is placed in an Agarwal bath. The resulting quantum master equations are studied with the help of quantum characteristic functions. The density matrix positivity is investigated in view of the recent interest in searching for a sound quantum dissipation theory. An analytical criterion is derived for density matrix negativity for two uncoupled oscillators. It is found that, for an initial two-oscillator squeezed state with a real squeezing parameter s, density matrix negativity occurs for two uncoupled oscillators at temperatures lower than \v/(kB ln cothusu) with v the oscillator frequency and kB the Boltzmann factor. As a by-product an analytical expression is also obtained for determining the quantum separability of two uncoupled oscillators. The effects of interoscillator coupling on density matrix negativity are discussed.