  We compare the average photospheric current helicity $H_c$, photospheric
twist parameter $\alpha$ (a well-known proxy for the full relative magnetic
helicity), and subsurface kinetic helicity $H_k$ for 194 active regions
observed between 2006-2013. We use 2440 Hinode photospheric vector
magnetograms, and the corresponding subsurface fluid velocity data derived from
GONG (2006-2012) and HMI (2010-2013) Dopplergrams. We find a significant
hemispheric bias in all three parameters. The subsurface kinetic helicity is
preferentially positive in the southern hemisphere and negative in the northern
hemisphere. The photospheric current helicity and the $\alpha$ parameter have
the same bias for strong fields ($|B|>1000$ G) and no significant bias for weak
fields (100 G $<|B|<500$ G). We find no significant region-by-region
correlation between the subsurface kinetic helicity and either the strong-field
current helicity or $\alpha$. Subsurface fluid motions of a given handedness
correspond to photospheric helicities of both signs in approximately equal
numbers. However, common variations appear in annual averages of these
quantities over all regions. Furthermore, in a subset of 77 regions we find
significant correlations between the temporal profiles of the subsurface and
photospheric helicities. In these cases, the sign of the linear correlation
coefficient matches the sign relationship between the helicities, indicating
that the photospheric magnetic field twist is sensitive to the twisting motions
below the surface.
