Let (X,Y) be bivariate normally distributed with mean (μ,v), var(X) = var(Y) = σ2, and correlation betweenXandYequal to ρ. Let (Xi,Yi) be independent observations on (X,Y) fori= 1, 2, · · ·,n. Because of practical considerations we observe onlyZi= min(Xi,Yi),i= 1, 2, · · ·,n. We are concerned with estimation and testing procedures when the parameter ρ is unknown. This model will be useful in certain studies of twins.