  A detailed canonical treatment of a new action for a nonrelativistic particle
coupled to background gravity, recently given by us, is performed both in the
Lagrangian and Hamiltonian formulations. The equation of motion is shown to
satisfy the geodesic equation in the Newton-Cartan background, thereby clearing
certain confusions. The Hamiltonian analysis is done in the gauge independent
as well as gauge fixed approaches, following Dirac's analysis of constraints.
The physical (canonical) variables are identified and the path to canonical
quantisation is outlined by explicitly deriving the Schroedinger equation.
