In Leicestershire there are several Parish Managed Libraries but the models vary. At Glen Hills the parish took over from the County Council in 2015 and there is a library sub committee. The library is entirely run by volunteers and the day to day running is through our Volunteer Working Group which reports to the sub committee.
There are also several CMLs that get a grant from their parish but are independently constituted organisations, which I think applies to you.
You might want to get in touch with some of them.