  We generalize the diffusive model for spin injection and detection in
nonlocal spin structures to account for spin precession under an applied
magnetic field in an anisotropic medium, for which the spin lifetime is not
unique and depends on the spin orientation.We demonstrate that the spin
precession (Hanle) line shape is strongly dependent on the degree of anisotropy
and on the orientation of the magnetic field. In particular, we show that the
anisotropy of the spin lifetime can be extracted from the measured spin signal,
after dephasing in an oblique magnetic field, by using an analytical formula
with a single fitting parameter. Alternatively, after identifying the
fingerprints associated with the anisotropy, we propose a simple scaling of the
Hanle line shapes at specific magnetic field orientations that results in a
universal curve only in the isotropic case. The deviation from the universal
curve can be used as a complementary means of quantifying the anisotropy by
direct comparison with the solution of our generalized model. Finally, we
applied our model to graphene devices and find that the spin relaxation for
graphene on silicon oxide is isotropic within our experimental resolution.
