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Abstract Measurements of the accelerations of stars enabled by time-series extreme-precision spectroscopic observations, pulsar timing, and eclipsing binary stars in the solar neighborhood offer insights into the mass distribution of the Milky Way that do not rely on traditional equilibrium modeling. Given the measured accelerations, we can determine a total mass density and infer the amount of dark matter (DM) by accounting for the mass in stars, gas, and dust. Leveraging FIRE-2 simulations of Milky Way–mass galaxies we compare vertical acceleration profiles between cold DM (CDM) and self-interacting DM (SIDM) with a constant cross section of 1 cm²g⁻¹across three halos with diverse assembly histories. Notably, significant asymmetries in vertical acceleration profiles near the midplane at fixed radii are observed in both CDM and SIDM, particularly in halos recently affected by mergers with satellites of Sagittarius/SMC-like masses or greater. These asymmetries offer a unique window into exploring the merger history of a galaxy. We show that SIDM halos manifest a more oblate shape and consistently exhibit higher local stellar and DM densities and steeper vertical acceleration gradients, up to 10%–30% steeper near the solar neighborhood. However, similar magnitude changes can arise from azimuthal variations in the baryonic components at a fixed radius and external influences like mergers, making it difficult to distinguish between CDM and SIDM using acceleration measurements in a single galaxy.