That every contract for highway improvement upon state roads or roads improved, maintained or constructed with state aid, under the provisions of this act, shall be made in the name of the state of New Mexico and signed by the state highway engineer, together with the board of county commissioners or other proper officer or officers of a participating county, and by the contracting party, and no such contract shall be entered into, nor shall any such work be authorized, in any county which will create a liability on the part of the state in excess of the funds apportioned to or otherwise available for expenditures in such county under the terms of this act.