A relationship between dust-reprocessed light from recent star formation and the amount of star-forming gas in a galaxy produces a correlation between Wide-field Infrared Survey Explorer (WISE) 12{mu}m emission and CO line emission. Here, we explore this correlation on kiloparsec scales with CO(1-0) maps from EDGE-CALIFA matched in resolution to WISE 12{mu}m images. We find strong CO-12{mu}m correlations within each galaxy and we show that the scatter in the global CO-12{mu}m correlation is largely driven by differences from galaxy to galaxy. The correlation is stronger than that between star formation rate and H_2_ surface densities [{Sigma}(H_2_)]. We explore multivariable regression to predict {Sigma}(H_2_) in star-forming pixels using the WISE 12{mu}m data combined with global and resolved galaxy properties, and provide the fit parameters for the best estimators. We find that {Sigma}(H_2_) estimators that include {Sigma}(12{mu}m) are able to predict {Sigma}(H_2_) more accurately than estimators that include resolved optical properties instead of {Sigma}(12{mu}m). These results suggest that 12{mu}m emission and H_2_ as traced by CO emission are physically connected at kiloparsec scales. This may be due to a connection between polycyclic aromatic hydrocarbon emission and the presence of H_2_. The best single-property estimator is log({Sigma}(H_2_)/M_{sun}_pc^-2^)= (0.48+/-0.01)+(0.71+/-0.01)log({Sigma}(12{mu}m)/L_{sun}_pc^-2^). This correlation can be used to efficiently estimate {Sigma}(H_2_) down to at least 1M_{sun}_pc^-2^ in star-forming regions within nearby galaxies.