In this paper a two-dimensional (2D) minimal circuit and state space realization is presented for a 2D continued fraction expansion of Roger-Ramanujan type. The proposed state space realization is based on the corresponding circuit implementation. For the state-space realization the 2D Roesser model of cycled structure is used. The dimension of the state vector, of the state space model, and the number of the delay elements, of the circuit realization, are absolutely minimal. Also minimal are the number of required multipliers. A step-by-step example is presented to illustrate the proposed results.