The local structure of La(Fei(1-x)Mn(x))AsO, showing suppression of long-range magnetic order by Mn-substitution, has been studied. Extended X-ray absorption fine structure (EXAFS) measurements at As K-edge and Fe K-edge are used to probe the atomic correlations in the FeAs-layer. We have found that both Fe-As and Fe-Fe bondlengths tend to increase with increasing Mn concentration. The associated mean square relative displacements (MSRD) reveal a gradual increase indicating increased local disorder in the FeAs-layer with Mn content. The results reveal that the FeAs-layer thickness, measured by the As-height (h(AS),) from the Fe-Fe plane, is correlated with the Neel temperature. Furthermore, Fe K beta X-ray emission spectroscopy (XES) shows a sharp increase in the Fe local magnetic moment with Mn substitution. The importance of the FeAs layer thickness in describing magnetic correlations in La(Fe1-xMnx)AsO is discussed.