  Neutral-current neutrino scattering from the deuteron leading to
proton-neutron final states is considered using an approach that incorporates
relativistic dynamics and consequently provides robust modeling at relatively
high energies and momenta. In this work the focus is placed on the fully
exclusive reaction where both the proton and neutron in the final state are
assumed to be detected. Accordingly, the incident neutrino energy, the neutrino
scattering angle and the scattered neutrino's energy can all be reconstructed.
It is shown that for specific choices of kinematics the reaction proceeds
mainly via scattering from the proton, while for other choices of kinematics it
proceeds mainly from the neutron. Specific asymmetries are introduced to focus
on these attributes. Measurements in both regions have the potential to yield
valuable information on the nucleon's electroweak form factors at momentum
transfers up to a (GeV/c)$^2$. In particular, the cross sections are shown to
be very sensitive to the isoscalar axial-vector form factor, and sensitive but
less so to the magnetic strangeness form factor. Comparisons with other
reactions, specifically charge-changing neutrino reactions and both
parity-conserving and -violating electron scattering, have the potential to
provide new ways to test the Standard Model.
