  The article is devoted to the nonparametric estimation of the quadratic
covariation of non-synchronously observed It\^o processes in an additive
microstructure noise model. In a high-frequency setting, we aim at establishing
an asymptotic distribution theory for a generalized multiscale estimator
including a feasible central limit theorem with optimal convergence rate on
convenient regularity assumptions. The inevitably remaining impact of
asynchronous deterministic sampling schemes and noise corruption on the
asymptotic distribution is precisely elucidated. A case study for various
important examples, several generalizations of the model and an algorithm for
the implementation warrant the utility of the estimation method in
applications.
