It's referred to here, in the 1999 election, so the law is at least that old.

Mid-term Legislative vacancies are filled by:



Appointment: The board of supervisors from the county of the vacating member's party select and certify a replacement. After this, the state supervisors of the predecessor's party confirm and certify the replacement. Next, the Secretary of State confirms the replacement, who is then sworn in. If the interim replacement occurs in the first year of the Assembly term or in the first three years of the senate term, then a special election will be held at the next general election. If the unexpired term has only one year left in the term, then the interim appointment will be satisfactory until the next general election.

Special Election: When a vacancy occurs at least 51 days prior to a regular general election, it shall be filled by appointment. The seat will come up for election at the next general election. If the vacancy occurs within 51 days of the general election, the seat shall remain vacant until the election occurs.



I'm not sure if this particular law applies to Senators or not, but the 51 number is the same.