  We present an analysis of new and archival VLA HI observations of a sample of
eleven early-type galaxies rich in CO, with detailed comparisons of CO and HI
distributions and kinematics. The early-type sample consists of both lenticular
and elliptical galaxies in a variety of environments. A range of morphologies
and environments were selected in order to give a broader understanding of the
origins, distribution, and fate of the cold gas in early-type galaxies. Six of
the eleven galaxies in the sample are detected in both HI and CO. The H$_{2}$
to HI mass ratios for this sample range from 0.2-120. The HI morphologies of
the sample are consistent with that of recent HI surveys of early-type galaxies
which also find a mix of HI morphologies and masses, low HI peak surface
densities, and a lack of HI in early-type galaxies which reside in high density
environments. The HI-detected galaxies have a wide range of HI masses
(1.4$\times10^{6}$ to 1.1$\times10^{10}$ M$_{\odot}$). There does not appear to
be any correlation between the HI mass and morphology (E versus S0). When HI is
detected, it is centrally peaked - there are no central kpc-scale central HI
depressions like those observed for early-type spiral galaxies at similar
spatial resolutions and scales. A kinematic comparison between the HI and CO
indicates that both cold gas components share the same origin. The primary goal
of this and a series of future papers is to better understand the relationship
between the atomic and molecular gas in early-type galaxies, and to compare the
observed relationships with those of spiral galaxies where this relationship
has been studied in depth.
