  We restrict a Siegel modular cusp form of degree 2 and square free level that
is a Yoshida lifting (a lifting from the orthogonal group of a definite
quaternion algebra) to the embedded product of two half planes and compute the
Petersson product against the product of two elliptic cuspidal Hecke
eigenforms. The square of this integral can be explicitly expressed in terms of
the central critical value of an L-function attached to the situation. The
result is related to a conjecture of Gross and Prasad about restrictions of
automorphic representations of special orthogonal groups.
