  We study some features of bosonic particle path-integral quantization in a
twistor-like approach by use of the BRST-BFV quantization prescription. In the
course of the Hamiltonian analysis we observe links between various
formulations of the twistor-like particle by performing a conversion of the
Hamiltonian constraints of one formulation to another. A particular feature of
the conversion procedure applied to turn the second-class constraints into the
first-class constraints is that the simplest Lorentz-covariant way to do this
is to convert a full mixed set of the initial first- and second-class
constraints rather than explicitly extracting and converting only the
second-class constraints. Another novel feature of the conversion procedure
applied below is that in the case of the D=4 and D=6 twistor-like particle the
number of new auxiliary Lorentz-covariant coordinates, which one introduces to
get a system of first-class constraints in an extended phase space, exceeds the
number of independent second-class constraints of the original dynamical
system. We calculate the twistor-like particle propagator in D=3, 4 and 6
space-time dimensions and show, that it coincides with that of a conventional
massless bosonic particle.
