We present measurements of the recoil proton polarization for the H-1((γ) over right arrow,(p) over right arrow)pi(0) reaction for theta(c.m.)(pi) = 60degrees-135degrees and for photon energies up to 4.1 GeV. These are the first data in this reaction for polarization transfer with circularly polarized photons. Various theoretical models are compared with the results. No evidence for hadron helicity conservation is observed. Models that employ factorization are not favored. It appears from the strong angular dependence of the induced polarization at photon energies of 2.5 and 3.1 GeV that a relatively high spin resonance or background amplitude might exist in this energy region.