Spoof attack by replicating biometric traits represents a real threat to an automatic biometric verification/ authentication system. This is because the system, originally designed to distinguish between genuine users from impostors, simply cannot distinguish between a replicated biometric sample (replica) from a live sample. An effective solution is to obtain some measures that can indicate whether or not a biometric trait has been tempered with, e.g., liveness detection measures. These measures are referred to as evidence of spoofing or anti-spoofing measures. In order to make the final accept/rejection decision, a straightforward solution to define two thresholds: one for the anti-spoofing measure, and another for the verification score. We compared two variants of a method that relies on applying two thresholds - one to the verification (matching) score and another to the anti-spoofing measure. Our experiments carried out using a signature database as well as by simulation show that both the brute-force and its probabilistic variant turn out to be optimal under different operating conditions.