  Optical rest-frame spectroscopic diagnostics are usually employed to
distinguish between star formation and AGN-powered emission. However, this
method is biased against dusty sources, hampering a complete census of the AGN
population across cosmic epochs. To mitigate this effect, it is crucial to
observe at longer wavelengths in the rest-frame near-infrared (near-IR), which
is less affected by dust attenuation and can thus provide a better description
of the intrinsic properties of galaxies. AGN diagnostics in this regime have
not been fully exploited so far, due to the scarcity of near-IR observations of
both AGNs and star-forming galaxies, especially at redshifts higher than 0.5.
Using Cloudy photoionization models, we identify new AGN - star formation
diagnostics based on the ratio of bright near-infrared emission lines, namely
[SIII] 9530 Angstrom, [CI] 9850 Angstrom, [PII] 1.188 $\mu m$, [FeII] $1.257
\mu m$, and [FeII] $1.64 \mu m$ to Paschen lines (either Pa$\gamma$ or
Pa$\beta$), providing simple, analytical classification criteria. We apply
these diagnostics to a sample of 64 star-forming galaxies and AGNs at 0 < z <
1, and 65 sources at 1 < z < 3 recently observed with JWST-NIRSpec in CEERS. We
find that the classification inferred from the near-infrared is broadly
consistent with the optical one based on the BPT and the [SII]/H$\alpha$ ratio.
However, in the near-infrared, we find $\sim 60 \%$ more AGNs than in the
optical (13 instead of 8), with 5 sources classified as 'hidden' AGNs, showing
a larger AGN contribution at longer wavelengths, possibly due to the presence
of optically thick dust. The diagnostics we present provide a promising tool to
find and characterize AGNs from z=0 to z=3 with low and medium-resolution
near-IR spectrographs in future surveys.
