In this paper, a stochastic geometry approach is used to model and analyse a downlink small cell network (SCN). Carrier sense multiple access with collision avoidance (CSMA/CA) is used as medium access control (MAC) protocol at the base stations (BSs). To boost spectral efficiency, each active BS deploys both orthogonal multiple access (OMA) and nonorthogonal multiple access (NOMA) to transmit signals to the user equipments (UEs) in its coverage area. The choice between OMA and NOMA mode is based on the density of UEs and aims to improve the sum rate of the BS. If there exist two UEs that sufficiently differ in their channel power gains to the BS, the BS will use NOMA superimposing the signals of the UEs in the power-domain. Otherwise, the BS will operate in OMA mode to transmit the signal of a single UE in its coverage area. Stochastic geometry is used to include the spatial densities of the UEs and BSs in the performance assessment of the SCN. On this basis, analytical expressions for the coverage probability, data rates of the UEs, and sum rate of the BSs of the considered system are derived. Numerical results are provided to illustrate the impact of system parameters on the performance of this SCN with NOMA subject to the spatial densities of the BSs and UEs.