shared roof - are both owners liable for repair costs

Is maintenance of a shared roof valley between adjoining terraced houses the joint responsibilty of both owners, even if water ingress only affects one property. Does maintenance of the roof valley fall under the Party Wall Act. In my circumstances, the valley is in a poor state of repair and requires replacing as there is water ingress affecting my property my neighbour is not really approachable so I don't know if her property is also affected. The gully needs replacing. My question is because it is a shared gully is my neighbour responsible for half of the cost of repair?

Thanks