Cal. Civ. Proc. Code § 583.120

(a) This chapter applies to a civil action and does not apply to a special proceeding except to the extent incorporated by reference in the special proceeding.
(b) Notwithstanding subdivision (a), the court may, by rule or otherwise under inherent authority of the court, apply this chapter to a special proceeding or part of a special proceeding except to the extent such application would be inconsistent with the character of the special proceeding or the statute governing the special proceeding.