We report on an experimental characterization of the sensitivity of localized surface plasmons (LSP) to local changes in the refractive index at a nanometer scale. The method is based on forming a polymer mask covering different well defined areas of metallic nanoparticles and measuring the extinction peak shifts associated with the local refractive index changes. Arrays of nanoparticles (nanorod chains) are prepared using electron beam lithography and the dielectric mask is aligned with respect to the nanoparticle array in a second lithographic step. Extinction peak shifts corresponding to different positions of the mask are measured and values for the local refractive index sensitivity are deduced. A deconvolution procedure is established and used to map the local sensitivity across the surface of nanoparticle based on measured data. The experimental results are shown to correspond well with theoretical simulations obtained using the finite-difference time-domain method. The results indicate that the sensitivity is strongly correlated with the profile of the LSP electric field.