  Using spectral-line observations of HNCO, N2H+, and HNC, we investigate the
kinematics of dense gas in the central ~250 pc of the Galaxy. We present SCOUSE
(Semi-automated multi-COmponent Universal Spectral-line fitting Engine), a line
fitting algorithm designed to analyse large volumes of spectral-line data
efficiently and systematically. Unlike techniques which do not account for
complex line profiles, SCOUSE accurately describes the {l, b, v_LSR}
distribution of CMZ gas, which is asymmetric about Sgr A* in both position and
velocity. Velocity dispersions range from 2.6 km/s<\sigma<53.1 km/s. A median
dispersion of 9.8 km/s, translates to a Mach number, M_3D>28. The gas is
distributed throughout several "streams", with projected lengths ~100-250 pc.
We link the streams to individual clouds and sub-regions, including Sgr C, the
20 and 50 km/s clouds, the dust ridge, and Sgr B2. Shell-like emission features
can be explained by the projection of independent molecular clouds in Sgr C and
the newly identified conical profile of Sgr B2 in {l ,b, v_LSR} space. These
features have previously invoked supernova-driven shells and cloud-cloud
collisions as explanations. We instead caution against structure identification
in velocity-integrated emission maps. Three geometries describing the 3-D
structure of the CMZ are investigated: i) two spiral arms; ii) a closed
elliptical orbit; iii) an open stream. While two spiral arms and an open stream
qualitatively reproduce the gas distribution, the most recent parameterisation
of the closed elliptical orbit does not. Finally, we discuss how proper motion
measurements of masers can distinguish between these geometries, and suggest
that this effort should be focused on the 20 km/s and 50 km/s clouds and Sgr C.
