The authors study a correlated-site percolation model on a square lattice in which a site is occupied if all four bonds surrounding it are occupied; this model is of possible relevance to supercooled H₂O and D₂O. Using Monte Carlo methods, they find the critical concentration of sites rho _c=0.562+or-0.001, and the critical exponents nu =1.33+or-0.07 and gamma =2.56+or-0.27. These results indicate that this correlated percolation problem is in the same universality class as uncorrelated percolation, while the critical threshold is decreased by about 5% relative to its value for the corresponding random-site percolation problems.