Scalar product on the space of conformal blocks

Question

Conformal blocks are extensively used as trial wave functions in the Quantum Hall Effect. The interpretation as wavefunctions implies that there is a scalar product on the space of relevant conformal blocks. Does this scalar product have any interpretation within the CFT framework, without reference to the Quantum Hall Effect?

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Addition: example for the sake of illustration and making the question more concrete. Conformal block is a function of $n$ points $B(z_1,\dots,z_n)$ which are interpreted as positions of particles in the QHE. Then for example the integral $\int d^2z_1\dots d^2z_n |B(z_1,\dots,z_n)|^2$ is a norm of the corresponding state. So, does this expression correspond to any known object in the original conformal field theory?