$\ensuremath{\gamma}$-ray linear polarization measurements have been used to locate negative parity states in the even-odd isotopes $^{99,101,103}\mathrm{Pd}$. A Compton polarimeter based on two Ge(Li) coaxial detectors was used. Collective bands ($I={\frac{11}{2}}^{\ensuremath{-}}, {\frac{15}{2}}^{\ensuremath{-}}, {\frac{19}{2}}^{\ensuremath{-}}, \dots{}$) built on ${\frac{11}{2}}^{\ensuremath{-}}$ states were observed in $^{101}\mathrm{Pd}$ and $^{103}\mathrm{Pd}$. Many negative parity states were also observed in $^{99}\mathrm{Pd}$, but they do not appear to be part of a similar collective band. These polarization measurements also confirm many angular momentum assignments which previously had been made using systematic arguments.NUCLEAR REACTIONS $^{90,92,94}\mathrm{Zr}(^{12}\mathrm{C}, 3n)$, $E=48\ensuremath{-}56$ MeV; measured linear polarization of $\ensuremath{\gamma}$ rays; parities and multipole mixing ratios in $^{99,101,103}\mathrm{Pd}$ transitions deduced.