The board may charge or assess each public agency and each public agency shall pay and reimburse the state at such times and in such amounts as the board may determine, the approximate cost to the state of any and all work and services relating to a division under Article 2.5 (commencing with Section 22150) of Chapter 1 or the referendum provided by Article 2 (commencing with Section 22300) of Chapter 2 and requested by the agency. The charges or assessments shall be determined by the board in a manner approved by the Department of Finance.