Human resource management is the management of the people who work for an organization. Change management is the art and science of facilitating changes at minimal cost and disruption. The connection between the two is in neverending changes in management and employment and the tendency of human resources, i.e. people, to not do very well with change.
Think of all the changes that an organization goes through. There are personnel changes, changes in equipment and technology, changes in location, changes in statutes and regulations that control the work environment, changes in scheduling and production, changes in services, changes in training and education, and so on.
I would think that it is the responsibility of both departments to ease all such transitions in an organization. Otherwise, changes which are meant to be beneficial can very well turn out to be detrimental. The overlapping responsibility probably causes one department or the other to drop the ball sometimes, so who is responsible for what should be delineated in a way that is as clear as possible.