  Recent calculations with an effective isospin dependent contact interaction
show the possibility of the crossover from superfluidity of neutron Cooper
pairs in $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of
di-neutron bound states in dilute nuclear matter. The density and spin
correlation functions are calculated for a di-neutron condensate in asymmetric
nuclear matter with the aim to find the possible features of the BCS-BEC
crossover. It is shown that the zero-momentum transfer spin correlation
function satisfies the sum rule at zero temperature. In symmetric nuclear
matter, the density correlation function changes sign at low momentum transfer
across the BCS-BEC transition and this feature can be considered as a signature
of the crossover. At finite isospin asymmetry, this criterion gives too large
value for the critical asymmetry $\alpha_c^d\sim0.9$, at which the BEC state is
quenched. Therefore, it can be trusted for the description of the
density-driven BCS-BEC crossover of neutron pairs only at small isospin
asymmetry.
  This result generalizes the conclusion of the study in Phys. Rev. Lett. {\bf
95}, 090402 (2005), where the change of sign of the density correlation
function at low momentum transfer in two-component quantum fermionic atomic gas
with the balanced populations of fermions of different species was considered
as an unambiguous signature of the BCS-BEC transition.
