  We identify the multiparameter sensitivity of split nonclassical spin states,
such as spin-squeezed and Dicke states spatially distributed into several
addressable modes. Analytical expressions for the spin-squeezing matrix of a
family of states that are accessible by current atomic experiments reveal the
quantum gain in multiparameter metrology, as well as the optimal strategies to
maximize the sensitivity. We further study the mode entanglement of these
states by deriving a witness for genuine $k$-partite mode entanglement from the
spin-squeezing matrix. Our results highlight the advantage of mode entanglement
for distributed sensing, and outline optimal protocols for multiparameter
estimation with nonclassical spatially-distributed spin ensembles.
