Several long-standing theories postulate that turbulent dissipation can heat solar wind protons in situ. Turbulent dissipation can occur via current sheets, which are small-scale structures embedded in the solar wind magnetic field. This study examines the role that switchbacks—intermediate-scale reversals in the interplanetary magnetic field—may play in heating the solar wind by generating current sheets. We explore this possible relationship by analyzing the characteristics of current sheets within and around switchback regions. Previous studies investigated current sheet properties during Parker Solar Probe's first solar encounter, analyzed current sheets using a wide range of statistics, and explored trends that switchbacks follow with radial distance from the Sun. The present study builds on these works by analyzing the distribution and maximum values of solar wind current sheets using the Partial Variance of Increments method and focusing on how these properties correlate with the presence of switchbacks to better understand how switchbacks contribute to current sheet activity. We conclude that there are no increased current sheet populations observed within and around switchbacks, with most current sheets being observed outside switchbacks. We find a consistent distribution of current sheets regardless of whether there is concurrent switchback activity. We also observe that current sheets follow a uniform occurrence rate with increased distance from the Sun, while switchback regions significantly evolve with larger radial distances. Our findings suggest that local turbulence may be responsible for generating solar wind current sheets and does so with the same efficiency inside and outside of switchback regions.