Gas-puff z-pinch plasmas are used as sources of radiation (x-ray or neutron) for applications such as imaging, and as test beds for understanding phenomena that affect larger-scale fusion power generation concepts. In both cases, it is vital to understand how the energy in the system is partitioned between various forms; for example, directed kinetic energy versus thermal energy versus non-directed turbulent kinetic energy. This thesis focuses on using a visible-light collective Thomson scattering diagnostic to determine the conditions in a neon gas-puff z-pinch plasma, specifically, the presence of plasma turbulence. This is the first successful use of the electron plasma wave (EPW) spectral feature for time-resolved density measurements in a gas-puff z-pinch, including a determination that turbulence in the implosion carries a significant fraction of the energy into the stagnation region. The z-pinch plasmas are produced by the COBRA pulsed power generator (with a rise time of ~240 ns and 0.9 MA peak current). A 526.5 nm, 10 J, 2.3 ns Thomson scattering diagnostic laser enables probing of the plasma conditions with \textless 1 mm spatial and on the order of 0.5 ns temporal resolution. The ion acoustic wave (IAW) Thomson scattering feature can routinely determine electron temperature ($Te$) and plasma flow velocity ($vk$), but the width of the IAW peaks depends on both ion temperature ($Ti$) and on fluid velocity distributions in the scattering volume. We observe that including a velocity distribution in the fitting model for the IAW profiles improves the fit (better describes what is occurring in the plasma) for a range of times from approximately 10 ns pre-pinch to 2 ns pre-pinch. The width of the velocity distribution does not scale with the size of the scattering volume, indicating that the distribution is not due to a continuous velocity gradient, but more likely from small-scale, non-directed hydrodynamic motion such as turbulent eddies. In order to further corroborate the presence of plasma turbulence, we turn to the EPW spectral feature of Thomson scattering. The EPW provides a second measurement of $Te$ as well as a measurement of electron density ($ne$). The width of the EPW depends on $Te$, but is also affected by non-uniform $ne$ in the scattering volume. We look for small-scale, local density variations in the plasma by comparing the values of $Te$ derived from the IAW and EPW. The presence of significant density variation is required because otherwise the main mechanism affecting the EPW width, Landau damping, would require too high a $Te$ to be reasonable given the $Te$ measured via the IAW. Large random velocity variation in the scattering volume is also required to obtain a good fit for the IAW in these cases. This comparison indicates the presence of regions of different density in the scattering volume. In conjunction with the velocity distributions observed in the IAW feature, this points to turbulent motion within the plasma. Based on the smaller but still present difference between $Te$(IAW) and $Te$(EPW) in the sheath, turbulence has begun to develop already in the imploding plasma. Once it reaches the axis, it has fully developed, showing up as a significant difference between $Te$(IAW) and $Te$(EPW) (the presence of regions of different density), and large velocity distributions.