  The second central extension of the planar Galilei group has been alleged to
have its origin in the spin variable. This idea is explored here by considering
local Galilean covariant field theory for free fields of arbitrary spin. It is
shown that such systems generally display only a trivial realization of the
second central extension. While it is possible to realize any desired value of
the extension parameter by suitable redefinition of the boost operator, such an
approach has no necessary connection to the spin of the basic underlying field.
