  We study both the intrinsic and extrinsic spin Hall effect in spin-valley
coupled monolayers of transition metal dichalcogenides. We find that whereas
the skew-scattering contribution is suppressed by the large band gap, the
side-jump contribution is comparable to the intrinsic one with opposite sign in
the presence of scalar and magnetic scattering. Intervalley scattering tends to
suppress the side-jump contribution due to the loss of coherence. By tuning the
ratio of intra- to intervalley scattering, the spin Hall conductivity shows a
sign change in hole-doped samples. Multiband effect in other doping regime is
considered, and it is found that the sign change exists in the heavily
hole-doped regime, but not in the electron-doped regime.
