We report on the determination of the difference in the refractive index between the ordinary and extraordinary rays in droplets of nematic liquid crystal E-44 at the wavelength of laser trapping, 1064 nm. This difference was calculated by measuring the ellipticity of laser tweezers for the moment at which rotation of the trapped droplet starts. The precision of this determination of the refractive index difference is approximately 5×10−3. Hydrophobic nematic liquid crystal E-44 formed 0.5–5-μm droplets when cast into D2O. The efficiency of the transfer of light torque to the liquid crystal droplets was determined to be 70% for the no-slip-boundary condition.