In this work we have studied the spin-lattice relaxation of $^{19}$F spins in benzotrifluoride in our quest for a reliable method of discriminating the contribution due to dipolar relaxation mechanism from that due to spin-rotational mechanism for nuclear spins located on methyl or substituted methyl group in organic molecules. Over the temperature range of 248-268 K the decay of normalized longitudinal magnetization was found to be well described by a two parameter equation of the form R(t) = exp(-st){$frac{5}{6}$exp(-s$_1$)+$frac{1}{6}$} which was derived under the assumption that interactions in the A3 spin system are modulated randomly and predominantly by internal rotational motions of -CF_3$ top, and it was shown that the separation of contribution due to dipolar interactions from that due to spin-rotation interaction could be successfully achieved by least-square fitting of observed data to this equation. The results indicate that the spin-rotational contribution is overwhelmingly larger than that of dipolar origin over the given temperature range and becomes more deminating at higher temperature