Using Zγ candidate events collected by the CDF detector at the Tevatron Collider, we search for potential anomalous (non-standard-model) couplings between the Z boson and the photon. Zγ couplings vanish at tree level and are heavily suppressed at higher orders; hence any evidence of couplings indicates new physics. Measurements are performed using data corresponding to an integrated luminosity of 4.9  fb−1 in the Z→νν decay channel and 5.1  fb−1 in the Z→l+l− (l=μ, e) decay channels. The combination of these measurements provides the most stringent limits to date on Zγ trilinear gauge couplings. Using an energy scale of Λ=1.5  TeV to allow for a direct comparison with previous measurements, we find limits on the CP-conserving parameters that describe Zγ couplings to be |hγ,Z3|<0.022 and |hγ,Z4|<0.0009. These results are consistent with standard model predictions.