By locally poling and measuring ultrathin films of the ferroelectric copolymer vinylidenefluoride/trifluoroethylene (VDF/TrFE), we show that the substrates on which these films are adsorbed play a strong role in orienting and poling the films. We carried out both poling and measurements using the Au-coated probe tip of the cantilever of an atomic force microscope. For ultrathin films of about 20 nm of the copolymer spin-coated on graphite, only a fraction of the thickness of the copolymer film can be repoled, so that the net local piezoelectric effect is enhanced or reduced, depending upon whether poling is parallel or antiparallel to that induced by the substrate, respectively. For sufficiently thick films, this substrate effect is negligible. The apparent lateral resolution with which information can be stored by poling in ultrathin films depends strongly on the film thickness and poling direction with respect to the substrate effect.