The production process of quarkonia in proton-proton ($pp$) collision is a very good probe of the parton structure of the proton.
Recent experimental data of the production of $J/\psi$+vector boson or quarkonium pairs at the LHC and Tevatron suggest the relevance of double parton scatterings (DPS).
We discuss here the single parton scattering (SPS) contribution to the $J/\psi +Z$, $J/\psi +W$, and $J/\psi +J/\psi$ productions in hadron collisions.
By revisiting the computations of the SPS contributions to the $J/\psi+Z$ and $J/\psi +W$ productions, we demonstrate that the ATLAS data in fact show evidence for DPS.