Dust attenuation affects nearly all observational aspects of galaxy evolution, yet very little is known about the form of the dust-attenuation law in the distant Universe. Here, we model the spectral energy distributions (SEDs) of galaxies at z = 1.5--3 from CANDELS with rest-frame UV to near-IR imaging under different assumptions about the dust law, and compare the amount of inferred attenuated light with the observed infrared (IR) luminosities. Some individual galaxies show strong Bayesian evidence in preference of one dust law over another, and this preference agrees with their observed location on the plane of infrared excess (IRX, $L_{text{TIR}}/L_{text{UV}}$) and UV slope ($beta$). We generalize the shape of the dust law with an empirical model, $A_{lambda,delta}=E(B-V) k_lambda (lambda/lambda_V)^delta$ where $k_lambda$ is the dust law of Calzetti et al. (2000), and show that there exists a correlation between the color excess ${E(B-V)}$ and tilt $delta$ with ${delta=(0.62pm0.05)log(E(B-V))}$+ ${(0.26~pm~0.02)}$. Galaxies with high color excess have a shallower, starburst-like law, and those with low color excess have a steeper, SMC-like law. Surprisingly, the galaxies in our sample show no correlation between the shape of the dust law and stellar mass, star-formation rate, or $beta$. The change in the dust law with color excess is consistent with a model where attenuation is caused by by scattering, a mixed star-dust geometry, and/or trends with stellar population age, metallicity, and dust grain size. This rest-frame UV-to-near-IR method shows potential to constrain the dust law at even higher ($z>3$) redshifts.
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