It is unclear from your question what do you mean by "separated
from the state". In fact European history knows only one
theocratic state - the area under direct papal control centered
in Rome, known at different periods as Papal states or Vatican.
The rulers of all other European states were secular persons.
Still the laws of many European states empathized Christianity
as the state religion or Christian god as the source of power.
In all European states the church performed some duties that now
viewed as the duty of state. For example, the registration of
births and marriages. But among population of different
confessions these duties were performed by different religious
bodies. For example, births and marriages among Jews were
registered by Jewish religious organizations. I will list some
events that may be relevant to your question. In the years 1103
to 1075 there was a dispute between the Pope and some of
European monarchs, notably, the Holy Roman Emperor over who has
the right to appoint church officia