Using particle simulations of the uniform shear flow of a rough dilutegranular gas, we show that the translational and rotational velocities arestrongly correlated in direction, but there is no orientationalcorrelation-induced singularity at perfectly smooth ($\beta=-1$) and rough($\beta=1$) limits for elastic collisions ($e=1$); both the translational androtational velocity distribution functions remain close to a Gaussian for thesetwo limiting cases. Away from these two limits, the orientational as well asspatial velocity correlations are responsible for the emergence of non-Gaussianhigh velocity tails. The tails of both distribution functions follow stretchedexponentials, with the exponents depending on normal ($e$) and tangential($\beta$) restitution coefficients.
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