Witten's asymptotic expansion conjecture as described in "Problems on invariants of knots and 3-manifolds" in Geometry and Topology Monographs, Volume 4 states that

$$Z_r^{SU(2)}(M)\sim_{r\rightarrow \infty} e^{-3\pi \bf{i}(1+b^1(M))/4}\times \sum_{[A]}e^{2\pi \bf{i}CS(A)} r^{(h^1_A-h^0_A)} e^{-2\pi \bf{i}(I_A/4+h^0_A/8)}\tau_M(A)^{1/2},$$

where $b^1(M)$ is the first betti number of $M$, $CS(A)$ is the chern-simons invariant of $A$, $h^i_A$ is the rank of the $i$th cohomology of $M$ with coefficients in the $su(2)$ bundle twisted by the adjoint action of the monodromy of $A$ and $I_A$ is the spectral flow of the Laplace operator along a path connecting $A$ to the trivial flat connection. Finally, $\tau_M(A)$ is the Reidemeister torsion.

Since $h^1$ is often the dimension of the Zariski tangent space of the space of gauge equivalence classes of flat connections, if $h^1>0$ in this formula, you are admitting the possibility that the moduli space of flat connections has positive dimension. In this case the sum is not really a sum, but an integral. The torsion in this case defines a volume form on $H_0(M,adA)\oplus H^1(M;adA)\oplus H_2(M,ad A)\oplus H^3(M,adA)$ ,where I mean the complex with twisted homology as appears above. Clearly what is meant by $\tau_M(A)^{1/2}$ must be a volume form on the moduli space of gauge equivalence classes of flat connections for the integral to work. That means $\tau_M(A)^{1/2}$ is a top dimensional form on $H^1(M;adA)$.

What is the explicit formula for the volume form? In other words, how do you go about cutting down the torsion and taking its square root as as a differential form?