Critical properties of the Calogero-Sutherland model of BCN-type (BCN-cs model) are studied. Using the asymptotic Bethe ansatz spectrum of the BCN-cs model, we calculate finite-size corrections in the energy spectrum. Since the BCN-cs model does not possess translational invariance, the finite-size spectrum acquires the contributions coming from 'boundaries'. We show that the low-energy critical behaviour of the model is described by c = I boundary conformal field theory. Thus the universality class of the model is identified as a chiral Tomonaga-Luttinger liquid.