  Majorana bound states are spatially localized superpositions of electron and
hole excitations in the middle of a superconducting energy gap. A single qubit
can be encoded nonlocally in a pair of spatially separated Majorana bound
states. Such Majorana qubits are in demand as building blocks of a topological
quantum computer, but direct experimental tests of the nonlocality remain
elusive. Here we propose a method to probe the nonlocality by means of crossed
Andreev reflection, which is the injection of an electron into one bound state
followed by the emission of a hole by the other bound state (equivalent to the
splitting of a Cooper pair over the two states). We have found that, at
sufficiently low excitation energies, this nonlocal scattering process
dominates over local Andreev reflection involving a single bound state. As a
consequence, the low-temperature and low-frequency fluctuations $\delta I_{i}$
of currents into the two bound states $i=1,2$ are maximally correlated:
$\overline{\delta I_{1}\delta I_{2}}=\overline{\delta I_{i}^{2}}$.
