The TIBER II blanket design is chosen for a neutronic sensitivity analysis using Monte Carlo perturbation theory. A preliminary analysis is carried out with both deterministic and Monte Carlo simulation codes to estimate the sensitivity of the tritium breeding in the blanket to the atomic density ratio of tungsten multiplier and aqueous solution breeder. Derivatives of the neutron collision density in the blanket are then sampled using the collision estimator in the MORSE code. It is found that for small perturbations, the neutron fluxes and tritium breeding rates can be predicted quite accurately, thus saving substantial computing in a preliminary design study.