We consider the Krein Laplacian on a regular bounded domain Omega subset of R-d, d >= 2, perturbed by a real-valued multiplier V vanishing on the boundary. Assuming that V has a definite sign, we investigate the asymptotics of the functions counting the eigenvalues of K +V which converge to the origin from below or from above. We show that the effective Hamiltonian that governs the main asymptotic term of these functions is the harmonic Toeplitz operator T-V with symbol V, unitarily equivalent to a pseudodifferential operator on the boundary. In the cases where V admits a power-like decay at partial derivative Omega, or V is compactly supported in Omega, and Omega and supp V are radially symmetric, we obtain the main asymptotic term of the eigenvalue counting functions.