The statistical distribution of the topologically constrained excitations in the close-packed dimer system on a finite planar square lattice is studied. The elementary excitations in the momentum space are shown to follow a generalized Fermi-Dirac distribution. In the projected momentum space, the excitations can be classified into various species of non-interacting superfermions, accompanied by certain statistical weights dependent on the momentum associated with each species. In a sufficiently large system, the excitations behave like semions in a certain intermediate temperature regime. Our results indicate that the statistics of quasi-particles may strongly depend on the way they are characterized.
