We present measurements of the local core-collapse supernova (CCSN) rate using SN discoveries from the Palomar Transient Factory (PTF). We use a Monte Carlo simulation of hundreds of millions of SN light-curve realizations coupled with the detailed PTF survey detection efficiencies to forward model the SN rates in PTF. Using a sample of 86 CCSNe, including 26 stripped-envelope SNe (SESNe), we show that the overall CCSN volumetric rate is r^mathrmCC_v=9.10_-1.27^+1.56times 10^-5, textSNe yr^-1, textMpc^-3, h_70^3 at = 0.028, and the SESN volumetric rate is r^mathrmSE_v=2.41_-0.64^+0.81times 10^-5, textSNe yr^-1, textMpc^-3, h_70^3 . We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using eight events at z ensuremathleq 0.2 of r^mathrmSLSN-I_v=35_-13^+25, textSNe yr^-1textGpc^-3, h_70^3 , which represents the most precise SLSN-I rate measurement to date. Using a simple cosmic star formation history to adjust these volumetric rate measurements to the same redshift, we measure a local ratio of SLSN-I to SESN of sim1/810^+1500_-94 , and of SLSN-I to all CCSN types of sim1/3500^+2800_-720 . However, using host galaxy stellar mass as a proxy for metallicity, we also show that this ratio is strongly metallicity dependent: in low- mass (logM_* < 9.5 M_ensuremathodot) galaxies, which are the only environments that host SLSN-I in our sample, we measure an SLSN-I to SESN fraction of 1/300^+380_-170 and 1/1700^+1800_-720 for all CCSN. We further investigate the SN rates a function of host galaxy stellar mass, and show that the specific rates of all CCSNe decrease with increasing stellar mass.