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DNA methylation occurs predominantly on cytosine-phosphate-guanine (CpG) dinucleotides in the mammalian genome, and the methylation landscape is maintained over mitotic cell division. It has been posited that coupling of maintenance methylation activity among neighbouring CpGs is critical to stability over cellular generations; however, the mechanism is unclear. We used mathematical models and stochastic simulation to analyse data from experiments that probe genome-wide methylation of nascent DNA post-replication in cells. We find that DNA methylation maintenance rates on individual CpGs are locally correlated, and the degree of this correlation varies by genomic regional context. By using theory of protein diffusion along DNA, we show that exponential decay of methylation rate correlation with genomic distance is consistent with enzyme processivity. Our results provide quantitative evidence of genome-wide methyltransferase processivity in vivo . We further developed a method to disentangle different mechanistic sources of kinetic correlations. From the experimental data, we estimate that an individual methyltransferase methylates neighbour CpGs processively if they are 36 basepairs apart, on average. But other mechanisms of coupling dominate for longer inter-CpG distances. Our study demonstrates that quantitative insights into enzymatic mechanisms can be obtained from replication-associated, cell-based genome-wide measurements, by combining data-driven statistical analyses with hypothesis-driven mathematical modelling.