  We report the first measurements of spin injection in to graphene through a
20 nm thick tungsten disulphide (WS$_2$) layer, along with a modified spin
relaxation time ({\tau}s) in graphene in the WS$_2$ environment, via spin-valve
and Hanle spin-precession measurements, respectively. First, during the
spin-injection into graphene through a WS$_2$-graphene interface, we can tune
the interface resistance at different current bias and modify the spin
injection efficiency, in a correlation with the conductivity-mismatch theory.
Temperature assisted tunneling is identified as a dominant mechanism for the
charge transport across the interface. Second, we measure the spin transport in
graphene, underneath the WS$_2$ crystal and observe a significant reduction in
the {\tau}s down to 17 ps in graphene in the WS$_2$ covered region, compared to
that in its pristine state. The reduced {\tau}s indicates the WS$_2$-proximity
induced additional dephasing of the spins in graphene.
