  We consider the problem of local correlations in the kicked, dual-unitary
coupled maps on D-dimensional lattices. We demonstrate that for D>=2, fully
dual-unitary systems exhibit ultra-local correlations: the correlations between
any pair of operators with local support vanish in a finite number of time
steps. In addition, for $D=2$, we consider the partially dual-unitary regime of
the model, where the dual-unitarity applies to only one of the two spatial
directions. For this case, we show that correlations generically decay
exponentially and provide an explicit formula for the correlation function
between the operators supported on two and four neighbouring sites.
