  On the basis of quasipotential approach to the bound state problem in QED we
calculate the vacuum polarization, relativistic, recoil, structure corrections
of orders $\alpha^5$ and $\alpha^6$ to the fine structure interval $\Delta
E^{fs}=E(2P_{3/2})-E(2P_{1/2})$ and to the hyperfine structure of the energy
levels $2P_{1/2}$ and $2P_{3/2}$ in muonic $^3_2He$ ion. The resulting values
$\Delta E^{fs}= 144803.15 \mu eV$, $\Delta \tilde E^{hfs}(2P_{1/2})=-58712.90
\mu eV$, $\Delta \tilde E^{hfs}(2P_{3/2})=-24290.69 \mu eV$ provide reliable
guidelines in performing a comparison with the relevant experimental data.
