We use medium-resolution JWST/NIRSpec observations from the Cosmic Evolution Early Release Science Survey to place the first constraints on dust attenuation and star formation based on Paschen lines for a sizable sample of 63 galaxies at redshifts z = 1.0-3.1. Our analysis indicates strong correlations between the Balmer decrement, H alpha/H beta, and line ratios that include Paschen lines (i.e., Pa alpha/H beta, Pa beta/H beta, and the Paschen decrement, Pa alpha/Pa beta), suggesting that the former is sensitive to the overall dust obscuration toward H ii regions in high-redshift galaxies. The line ratios are used to derive nebular reddening, E(B - V)(neb), and star formation rates (SFRs). There is marginal evidence that the SFRs deduced from Paschen lines may exceed by approximate to 25% those derived from Balmer lines alone, suggesting the presence of star formation that is optically thick in Balmer lines, though deeper observations are needed to confirm this result. Using the Paschen-line constraints on the bolometric SFRs, we reevaluate the relationship between dust obscuration and UV spectral slope, and find a reddening of the UV continuum that, on average, follows the SMC extinction curve. This analysis highlights the need for deeper spectroscopy of more representative samples to evaluate nebular dust attenuation and bolometric SFRs in high-redshift galaxies, and their relationship to the reddening of the UV continuum.