The secretary is hereby authorized to enter into agreements with the proper Federal authorities and with the authorities of cities of the third class and with the authorities of counties covering the construction, replacement or repair of bridges as authorized by this act. Any city or county with which such an agreement is made shall agree therein to pay to the State Treasurer before any contract is awarded as herein provided a sum stated and agreed upon in such agreement as the city's or county's share of the cost, and said sum or sums when so paid shall be deposited by the State Treasurer in a special account in the Motor License Fund, from which special account payments on the contract shall be made on proper requisition of the department. If the initial amount deposited by any city or county is insufficient to pay the city's or county's share of any project, the city or county shall make such additional deposits as may be necessary to pay the city's or county's total share of the cost, and any balance remaining in such special account after payment of the final moneys to the contractor shall be repaid to the city or county upon proper requisition of the department.