We use James Webb Space Telescope Near-Infrared Camera Wide Field Slitless Spectroscopy (NIRCam WFSS) and the Near-Infrared spectrograph (NIRSpec) in the Cosmic Evolution Early Release survey to measure rest-frame optical emission-line ratios of 155 galaxies at z>2. The blind NIRCam grism observations include a sample of galaxies with bright emission lines that were not observed on the NIRSpec masks. We study the changes of the H{alpha}, [OIII]/H{beta}, and [NeIII]/[OII] emission lines in terms of redshift by comparing to lower-redshift SDSS, CLEAR, and MOSDEF samples. We find a significant (>3{sigma}) correlation between [OIII]/H{beta} with redshift, while [NeIII]/[OII] has a marginal (2{sigma}) correlation with redshift. We compare [OIII]/H{beta} and [NeIII]/[OII] to stellar mass and H{beta} SFR. We find that both emission-line ratios have a correlation with H{beta} SFR and an anticorrelation with stellar mass across the redshifts 0<z<9. Comparison with MAPPINGS V models indicates that these trends are consistent with lower metallicity and higher ionization in low-mass and high-SFR galaxies. We additionally compare to IllustrisTNG predictions and find that they effectively describe the highest [OIII]/H{beta} ratios observed in our sample, without the need to invoke MAPPINGS models with significant shock ionization components.