  We demonstrate the parallel and non-destructive readout of the hyperfine
state for optically trapped $^{87}$Rb atoms. The scheme is based on
state-selective fluorescence imaging and achieves detection fidelities $>$98%
within 10$\,$ms, while keeping 99% of the atoms trapped. For the read-out of
dense arrays of neutral atoms in optical lattices, where the fluorescence
images of neighboring atoms overlap, we apply a novel image analysis technique
using Bayesian inference to determine the internal state of multiple atoms. Our
method is scalable to large neutral atom registers relevant for future quantum
information processing tasks requiring fast and non-destructive readout and can
also be used for the simultaneous read-out of quantum information stored in
internal qubit states and in the atoms' positions.
