  We systematically derive an action for a nonrelativistic spinning partile in
flat background and discuss its canonical formulation in both Lagrangian and
Hamiltonian approaches. This action is taken as the starting point for deriving
the corresponding action in a curved background. It is achieved by following
our recently developed technique of localising the flat space galilean symmetry
\cite{BMM1, BMM3, BMM2}. The coupling of the spinning particle to a
Newton-Cartan background is obtained naturally. The equation of motion is found
to differ from the geodesic equation, in agreement with earlier findings.
Results for both the flat space limit and the spinless theory (in curved
background) are reproduced. Specifically, the geodesic equation is also
obtained in the latter case.
