  The physical phase space of the relativistic top, as defined by Hanson and
Regge, is expressed in terms of canonical coordinates of the Poincar\'e group
manifold. The system is described in the Hamiltonian formalism by the mass
shell condition and constraints that reduce the number of spin degrees of
freedom. The constraints are second class and are modified into a set of first
class constraints by adding combinations of gauge fixing functions. The
Batalin-Fradkin-Vilkovisky (BFV) method is then applied to quantize the system
in the path integral formalism in Hamiltonian form. It is finally shown that
different gauge choices produce different equivalent forms of the constraints.
