  We characterize the irreducible, admissible, spherical representations of
GSp(4,F) (where F is a p-adic field) that occur in certain CAP representations
in terms of relations satisfied by their spherical vector in a special Bessel
model. These local relations are analogous to the Maass relations satisfied by
the Fourier coefficients of Siegel modular forms of degree 2 in the image of
the Saito-Kurokawa lifting. We show how the classical Maass relations can be
deduced from the local relations in a representation theoretic way, without
recourse to the construction of Saito-Kurokawa lifts in terms of Fourier
coefficients of half-integral weight modular forms or Jacobi forms. As an
additional application of our methods, we give a new characterization of
Saito-Kurokawa lifts involving a certain average of Fourier coefficients.
