We present measurements of the local core collapse supernova (SN) 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 core collapse SNe, including 26 stripped-envelope SNe (SESNe), we show that the overall core collapse SN volumetric rate is $r^mathrm{CC}_v=9.10_{-1.27}^{+1.56}times10^{-5},text{SNe yr}^{-1},text{Mpc}^{-3}, h_{70}^{3}$ at $ langle z rangle = 0.028$, and the SESN volumetric rate is $r^mathrm{SE}_v=2.41_{-0.64}^{+0.81}times10^{-5}, text{SNe yr}^{-1},text{Mpc}^{-3}, h_{70}^{3}$. We further measure a volumetric rate for hydrogen-free superluminous SNe (SLSNe-I) using 8 events at $z{le}0.2$ of $r^mathrm{SLSN-I}_v=35_{-13}^{+25}, text{SNe yr}^{-1}text{Gpc}^{-3}, h_{70}^{3}$, 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 $sim 1/3500^{+2800}_{-720}$. However, using host galaxy stellar mass as a proxy for metallicity, we also show that this ratio is strongly metallicity dependent: in low-mass ($mathrm{log} M_{*} < 9.5 mathrm{M}_odot$) galaxies, which are the only environments that host SLSN-I in our sample, we measure a 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 core collapse SNe decrease with increasing stellar mass.
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