In case a landowner desires to erect a partition hedge or fence when the owner of the adjoining land is not liable to contribute thereto, the fence viewers may assign to each owner the part which the owner shall erect, maintain, rebuild, and repair, trim or cut back, by pursuing the method provided in sections 359A.3 and 359A.4; but the adjoining owner shall not be required to contribute thereto until the adjoining owner becomes liable so to do, as elsewhere in this chapter provided.