  Nonlocal correlations are useful for device independent (DI) randomness
certification [Nature (London) {\bf 464}, 1021 (2010)]. The advantage of this
DI protocol over the conventional quantum protocol is that randomness can be
certified even when experimental apparatuses are not trusted. Quantum
entanglement is the necessary physical source for the nonlocal correlation
required for such DI task. However, nonlocality and entanglement are distinct
concepts. There exist entangled states which produce no nonlocal correlation
and hence are not useful for the DI randomness certification task. Here we
introduce the measurement-device-independent randomness certification task
where one has trusted quantum state preparation device but the measurement
devices are completely unspecified. Interestingly we show that there exist
entangled states, with local description, that are useful resource in such task
which otherwise are useless in corresponding DI scenario.
