We have performed mu+SR studies on single-crystal URu2Si2 in the temperature range 0.05-300 K. Zero-field (ZF) measurements show an increase in relaxation rate below T(N) = 17.5 K. Transverse-field (TF) measurements in H = 2900 G along the a and c directions display a strongly anisotropic Knight shift which does not scale with the bulk susceptibility for T < 50 K. Low- T measurements reveal a penetration depth of approximately 7000-10 000 angstrom with a temperature-dependent linewidth in which two steps are observed near 0.3 and 0.9 K.