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We work out finite-dimensional integral formulae for the scalar product ofgenus one states of the group $G$ Chern-Simons theory with insertions of Wilsonlines. Assuming convergence of the integrals, we show that unitarity of theelliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalarproduct of CS states is closely related to the Bethe Ansatz for the commutingHamiltonians building up the connection and quantizing the quadraticHamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil

Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems