The propagator and corresponding path integral for a system of identic
al particles obeying parastatistics are derived, It is found that the
statistical weights of topological sectors of the path integral for pa
rafermions and parabosons are simply related through multiplication by
the parity of the permutation of the final positions of the particles
. Appropriate generalizations of statistics are proposed obeying unita
rity and factorizability (strong cluster decomposition). The realizati
on of simple maximal occupancy (Gentile) statistics is shown to requir
e ghost states.