Schramm's Locality Conjecture asserts that the value of the critical percolation parameter p_c of a graph satisfying p_c<1 depends only on its local structure. In this note, we prove this conjecture in the particular case of transitive graphs with polynomial growth. Our proof relies on two recent works about such graphs, namely supercritical sharpness of percolation by the same authors and a finitary structure theorem by Tessera and Tointon.
