  We present results from our SMA observations and data analyses of the SMA
archival data of the Class I protostar IRAS 04169+2702. The high-resolution
(~0.5") $^{13}$CO (3-2) image cube shows a compact ($r$ ~< 100 au) structure
with a northwest (blue) to southeast (red) velocity gradient, centered on the
0.9-mm dust-continuum emission. The direction of the velocity gradient is
orthogonal to the axis of the molecular outflow as seen in the SMA $^{12}$CO
(2-1) data. A similar gas component is seen in the SO (6$_5$-5$_4$) line. On
the other hand, the C$^{18}$O (2-1) emission traces a more extended ($r$ ~400
au) component with the opposite, northwest (red) to southeast (blue) velocity
gradient. Such opposite velocity gradients in the different molecular lines are
also confirmed from direct fitting to the visibility data. We have constructed
models of a forward-rotating and counter-rotating Keplerian disk and a
protostellar envelope, including the SMA imaging simulations. The
counter-rotating model could better reproduce the observed velocity channel
maps, although we could not obtain statistically significant fitting results.
The derived model parameters are; Keplerian radius of 200 au, central stellar
mass of 0.1 $M_{solar}$, and envelope rotational and infalling velocities of
0.20 km s$^{-1}$ and 0.16 km s$^{-1}$, respectively. One possible
interpretation for these results is the effect of the magnetic field in the
process of disk formation around protostars, $i.e.$, Hall effect.
