We perform the Hamiltonian analysis for a nonprojectable Ho\ifmmode \check{r}\else \v{r}\fi{}ava model whose potential is composed of $R$ and ${R}^{2}$ terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Ho\ifmmode \check{r}\else \v{r}\fi{}ava theory, the validity of the full nonprojectable theory still remains unanswered.