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We study the tunneling probability of a massive ($m_w$) uncharged scalarpacket out from a near-extremal, static charged black hole (with mass $M$ andcharge $Q\lesssim M$). We show that there is indeed a net probability that amassive uncharged particle tunnels out from the black hole so that the finalstate (with new mass $M'\equiv M-m_w < Q$) does violate the cosmic censorshipconjecture. Nevertheless, the typical time for such a black hole to discharge(i.e, to absorb charge $-Q$ from its surroundings and then become neutral) ismuch smaller than the tunneling time; therefore, the violation is neverattained in practice. Even for a completely isolated black hole (should itexist), the standard time dilation near the horizon stretches the typicalviolation time scale to unobservable values.

Massive scalar wave packet emission by a charged Black Hole and Cosmic Censorship Conjecture violation