Streets and Highways Code § 946
CHAPTER 2. Powers and Duties of Boards of Supervisors
No liability shall be created against the county in connection with any such improvement conducted by a city unless the board, by resolution, determines and declares the amount to be expended and directs that such sum be set apart and reserved out of any moneys available for such purpose in the general fund of the county, to be used exclusively for paying the expense of such improvement.