Neutron production in giga electron volt-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 Phases I and II respectively. The neutron production is measured as a function of the visible energy of the neutrino interaction and, for charged current quasielastic interaction candidates, also as a function of the neutrino energy. This study is also performed by classifying the complete sample into two pairs of event categories: charged current quasielastic and non charged current quasielastic, 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.