  For a nonseparable bipartite quantum state violating the
Clauser-Horne-Shimony-Holt (CHSH) inequality, we evaluate amounts of noise
breaking the quantum character of its statistical correlations under any
generalized quantum measurements of Alice and Bob. Expressed in terms of the
reduced states, these new threshold bounds can be easily calculated for any
concrete bipartite state. A noisy bipartite state, satisfying the extended CHSH
inequality and the perfect correlation form of the original Bell inequality for
any quantum observables, neither necessarily admits a local hidden variable
model nor exhibits the perfect correlation of outcomes whenever the same
quantum observable is measured on both "sides".
