The centrifugal nuclear thermal rocket is a concept for a liquid-fueled nuclear system that would allow for a much higher specific impulse than the more traditional solid-fueled nuclear thermal propulsion designs. Although some preliminary neutronics analyses have been done on conceptual designs, this work seeks to perform a more systematic analysis and optimization of design parameters and to investigate additional neutronics properties such as power distributions and reactivity coefficients. This work used OpenMC for neutronics analysis and Dakota for the parametric study and optimization. Inter- and intra-fuel element power distributions were calculated, and a strong radial dependence was noted within fuel elements that may pose a challenge to thermal constraints. A positive moderator temperature coefficient of 3.78 0.16 pcm/K was calculated for the reference model, which may pose a challenge for system design and control. The optimization study of reflector size, fuel spacing, fuel mass, and fuel element radius indicated many trade-offs in the design considerations, and that the baseline model can be significantly improved in all respects. Positive reactivity feedback can be minimized by reducing moderation, and peaking factors can be reduced by limiting the amount of fuel per fuel element, which also minimizes the system mass.