  We calculate the effect of nonmagnetic impurity scattering on the
spin-lattice relaxation rate in two-band superconductors with the s-wave
pairing symmetry. It is found that for the interaction parameters appropriate
for MgB2 the Hebel-Slichter peak is suppressed by disorder in the limit of
small interband impurity scattering rate. In the limit of strong impurity
scattering, when the gap functions in the two bands become nearly equal, the
single-band behavior is recovered with a well-defined coherence peak just below
the transition temperature.
