  We perform the Hamiltonian analysis of non-relativistic covariant
Horava-Lifshitz gravity in the formulation presented recently in
arXiv:1009.4885. We argue that the resulting Hamiltonian structure is in
agreement with the original construction of non-relativistic covariant
Ho\v{r}ava-Lifshitz gravity presented in arXiv:1007.2410. Then we extend this
construction to the case of RFDiff invariant Ho\v{r}ava-Lifshitz theory. We
find well behaved Hamiltonian system with the number of the first and the
second class constraints that ensure the correct number of physical degrees of
freedom of gravity.
