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Church of England, although sometimes described as a Catholic Church, is not the same as the Roman Catholic Church which is what I assume you mean by Catholicism. By way of trivial example, city of Liverpool has both Anglican (Church of England) and Roman Catholic cathedrals.
From what I can ascertain, the equivalent of the Church of England in USA is the Episcopal Church. See: http://en.wikipedia.org/wiki/Episcopal_Church_(United_States)
It is part of the Anglican Community which gives its ties with the Church of England.
Of course, in the USA the Roman Catholic Church is the same as the Roman Catholic Church throughout the world with its allegiance to the Vatican and the Pope.