Equivalence of forward and backward laws on $C([0,T], \mathbb R^n)$ for hypoelliptic diffusions

Consider a time-homogeneous diffusion process on $$\mathbb R^n$$ $$dX_t = b(X_t)dt + \sigma(X_t)dW_t$$ and suppose that it satisfies Hormander's Lie bracket condition. Suppose that it is stationary at a measure $$\rho(x)dx$$ with strictly positive density $$\rho$$.

Provided that $$b, \sigma$$ are sufficiently nice, the time-reversed process $$Y_t := X_{T-t}$$ satisfies

$$dY_t= -b(Y_t)dt + \sigma \sigma^T \nabla \log \rho(Y_t)dt + \sigma(Y_t)dW_t$$

Denote by $$P^+, P^-$$ the laws on path space $$C([0,T], \mathbb R^n)$$.

In the uniformly elliptic case ($$\sigma \sigma^T \succ \lambda I, \lambda \in \mathbb R$$), it is relatively easy to show, using Cameron-Martin-Girsanov's formula that $$P^+$$ and $$P^-$$ are equivalent. However, I have not been able to use the CMG formula when I drop the ellipticity assumption.

Is there another way to see whether these measures are equivalent in the hypoelliptic case? Any reference or hint would be of great help.