We report the ro-vibrational spectrum of the nu(3)(e') band of the methyl radical (CH3) solvated in superfluid He-4 nanodroplets. Five allowed transitions produce population in the N-K = 0(0), 1(1), 1(0), 2(2) and 2(0) rotational levels. The observed transitions exhibit variable Lorentzian line shapes, consistent with state specific homogeneous broadening effects. Population relaxation of the 00 and I, levels is only allowed through vibrationally inelastic decay channels, and the P-P(1)(1) and R-R(0)(0) transitions accessing these levels have 4.12(1) and 4.66(1) GHz full-width at half-maximum line widths, respectively. The line widths of the R-P(1) and R-R(1)(1) transitions are comparatively broader (8.6(1) and 57.0(6) GHz, respectively), consistent with rotational relaxation of the 2(0) and 2(2) levels within the vibrationally excited manifold. The nuclear spin symmetry allowed rotational relaxation channel for the excited 1(0) level has an energy difference similar to those associated with the 2(0) and 2(2) levels. However, the (P)Q(1)(1) transition that accesses the 1(0) level is 2.3 and 15.1 times narrower than the R-P(1)(1) and R-R(1)(1) lines, respectively. The relative line widths of these transitions are rationalized in terms of the anisotropy in the He-CH3 potential energy surface, which couples the molecule rotation to the collective modes of the droplet.