  A conditional symmetry is defined, in the phase-space of a quadratic in
velocities constrained action, as a simultaneous conformal symmetry of the
supermetric and the superpotential. It is proven that such a symmetry
corresponds to a variational (Noether) symmetry.The use of these symmetries as
quantum conditions on the wave-function entails a kind of selection rule. As an
example, the minisuperspace model ensuing from a reduction of the Einstein -
Hilbert action by considering static, spherically symmetric configurations and
r as the independent dynamical variable, is canonically quantized. The
conditional symmetries of this reduced action are used as supplementary
conditions on the wave function. Their integrability conditions dictate, at a
first stage, that only one of the three existing symmetries can be consistently
imposed. At a second stage one is led to the unique Casimir invariant, which is
the product of the remaining two, as the only possible second condition on
$\Psi$. The uniqueness of the dynamical evolution implies the need to identify
this quadratic integral of motion to the reparametrisation generator. This can
be achieved by fixing a suitable parametrization of the r-lapse function,
exploiting the freedom to arbitrarily rescale it. In this particular
parametrization the measure is chosen to be the determinant of the supermetric.
The solutions to the combined Wheeler - DeWitt and linear conditional symmetry
equations are found and seen to depend on the product of the two "scale
factors"
