N.J. Stat. Ann. § 27:8-3

All work done with federal aid shall be done and paid for as provided by law, except as to the division of cost. The balance of the cost, after deducting the amount received or to be received as federal aid, shall be divided between the state and any governing body or bodies taking part therein in such manner as may be agreed between the commissioner and such body or bodies, but the state's share shall in no case exceed fifty per cent of such balance.