Neutron production in GeV-scale neutrino interactions is a poorly studied process. We have measured the neutron multiplicities in atmospheric neutrino interactions in the Sudbury Neutrino Observatory experiment and compared them to the prediction of a Monte Carlo simulation using GENIE and a minimally modified version of GEANT4. We analyzed 837 days of exposure corresponding to Phase I, using pure heavy water, and Phase II, using a mixture of Cl in heavy water. Neutrons produced in atmospheric neutrino interactions were identified with an efficiency of $15.3\%$ and $44.3\%$, for Phase I and II respectively. The neutron production is measured as a function of the visible energy of the neutrino interaction and, for charged current quasi-elastic interaction candidates, also as a function of the neutrino energy. This study is also performed classifying the complete sample into two pairs of event categories: charged current quasi-elastic and non charged current quasi-elastic, and $\nu_{\mu}$ and $\nu_e$. Results show good overall agreement between data and Monte Carlo for both phases, with some small tension with a statistical significance below $2\sigma$ for some intermediate energies.