Should the department find that the state of New York properly should bear a part of the cost of any river improvement, it is hereby authorized to so recommend to the Legislature and it may not proceed further with the project until the Legislature has made the necessary provisions for the payment of such costs or unless the project be so modified as to eliminate state contributions to the cost thereof. Except under the above circumstances the state shall be liable for no costs in connection with any such improvement except that the salaries and general expenses of the members of the department not specifically assigned to the particular project are not to be assessed upon the district.