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We compile a catalogue of low-mass and high-mass X-ray binaries, somerecently reported binaries that likely host a neutron star (NS) or a black hole(BH), and binary pulsars (a pulsar and a non-degenerated companion) that havemeasured systemic radial velocities ($\gamma$). Using Gaia and radio propermotions together with $\gamma$, we integrate their Galactic orbits and infertheir post-supernova (post-SN) 3D peculiar velocities ($v_\mathrm{pec}^{z=0}$at Galactic plane crossing); these velocities bear imprint of natal kicks thatcompact objects received at birth. With the sample totalling 85 objects, wemodel the overall distribution of $v_\mathrm{pec}^{z=0}$ and find atwo-component Maxwellian distribution with a low- ($\sigma_v \approx21\,\mathrm{km~s^{-1}}$) and a high-velocity ($\sigma_v \approx107\,\mathrm{km~s^{-1}}$) component. A further comparison between distributionsof binary subgroups suggests that binaries hosting high-mass donors/luminouscompanions mostly have $v_\mathrm{pec}^{z=0}\lesssim 100\,\mathrm{km~s^{-1}}$,while binaries with low-mass companions exhibit a broader distribution thatextends up to $\sim 400\,\mathrm{km~s^{-1}}$. We also find significantanti-correlations of $v_\mathrm{pec}^{z=0}$ with binary total mass($M_\mathrm{tot}$) and orbital period ($P_\mathrm{orb}$), at over 99%confidence. Specifically, our fit suggests $v_\mathrm{pec}^{z=0}\proptoM_\mathrm{tot}^{-0.5}$ and $v_\mathrm{pec}^{z=0}\propto P_\mathrm{orb}^{-0.2}$.Discussions are presented on possible interpretation of the correlations in thecontext of kinematics and possible biases. The sample should enable a range offollow-up studies on compact object binary kinematics and evolution.

Evidence for mass-dependent peculiar velocities in compact object binaries: Towards better constraints on natal kicks