  We study $S=1$ spin liquid states on the kagome lattice constructed by
Gutzwiller-projected $p_x+ip_y$ superconductors. We show that the obtained spin
liquids are either non-Abelian or Abelian topological phases, depending on the
topology of the fermionic mean-field state. By calculating the modular matrices
$S$ and $T$, we confirm that projected topological superconductors are
non-Abelian chiral spin liquid (NACSL). The chiral central charge and the spin
Hall conductance we obtained agree very well with the $SO(3)_1$ (or,
equivalently, $SU(2)_2$) field theory predictions. We propose a local
Hamiltonian which may stabilize the NACSL. From a variational study we observe
a topological phase transition from the NACSL to the $Z_2$ Abelian spin liquid.
