We use the first compilation of 72 core-collapse supernovae (SNe) from the Palomar Transient Factory (PTF) to study their observed subtype distribution in dwarf galaxies compared to giant galaxies. Our sample is the largest single-survey, untargeted, spectroscopically classified, homogeneous collection of core- collapse events ever assembled, spanning a wide host-galaxy luminosity range (down to M$_r$ ≈ -14 mag) and including a substantial fraction (>20%) of dwarf (M$_r$ >= -18 mag) hosts. We find more core-collapse SNe in dwarf galaxies than expected and several interesting trends emerge. We use detailed subclassifications of stripped-envelope core-collapse SNe and find that all Type I core-collapse events occurring in dwarf galaxies are either SNe Ib or broad-lined SNe Ic (SNe Ic-BL), while normal'' SNe Ic dominate in giant galaxies. We also see a significant excess of SNe IIb in dwarf hosts. We hypothesize that in lower metallicity hosts, metallicity-driven mass loss is reduced, allowing massive stars that would have appeared as normal’’ SNe Ic in metal-rich galaxies to retain some He and H, exploding as Ib/IIb events. At the same time, another mechanism allows some stars to undergo extensive stripping and explode as SNe Ic-BL (and presumably also as long-duration gamma-ray bursts). Our results are still limited by small-number statistics, and our measurements of the observed N(Ib/c)/N(II) number ratio in dwarf and giant hosts (0.25$^+0.3$ $_-0.15$ and 0.23$^+0.11$ $_-0.08$, respectively; 1σ uncertainties) are consistent with previous studies and theoretical predictions. As additional PTF data accumulate, more robust statistical analyses will be possible, allowing the evolution of massive stars to be probed via the dwarf-galaxy SN population.