In this paper, we propose an NxN rearrangeable nonblocking (RNB) multicast free space optical (FSO) switch using non-movable tri-state switching elements (T-SEs). The proposed switch exhibits an optimal hardware complexity as it requires only N(N+1)/2 switching elements. The switch is analyzed and compared to existing optical multicast switches in terms of hardware complexity, power loss, and cost. Comparison results show that the proposed switch provides multicast capability with a lower hardware complexity and a comparable performance. Cost analysis shows that, for N=4, the overall cost of the new design is lower than that of existing SNB switches even if the T-SE is 4 to 10 times the cost of typical MEMS mirrors. In addition, we present a simple routing algorithm that systematically establishes connections over the new switch.