Recent studies of optical reflectors as part of the vision apparatus in the eyes of decapod crustaceans revealed assemblies of nanoscale spherulites - spherical core-shell nanoparticles with radial birefringence. Simulations performed on the system highlighted the advantages of optical anisotropy in enhancing the functionality of these structures. So far, calculations of the nanoparticle optical properties have relied on refractive indices obtained using ab-initio calculations. Here we describe a direct measurement of the tangential refractive index of the spherulites, which corresponds to the in-plane refractive index of crystalline isoxanthopterin nanoplatelets. We utilize measurements of scattering spectra of individual spherulites and determine the refractive index by analyzing the spectral signatures of scattering resonances. Our measurements yield a median tangential refractive index of 1.88, which is in reasonable agreement with theoretical predictions. Furthermore, our results indicate that the optical properties of small spherulite assemblies are largely determined by the tangential index.