California Code, Education Code - EDC § 48011

A child who, consistent with Section 48000, has been admitted to the kindergarten maintained by a private or a public school in California or any other state, and who has completed one school year therein, shall be admitted to the first grade of an elementary school unless the parent or guardian of the child and the school district agree that the child may continue in kindergarten for not more than an additional school year.

A child who has been lawfully admitted to a public school kindergarten or a private school kindergarten in California and who is judged by the administration of the school district, in accordance with rules and regulations adopted by the State Board of Education, to be ready for first-grade work may be admitted to the first grade at the discretion of the school administration of the district and with the consent of the child's parent or guardian if the child is at least five years of age. When a child has been legally enrolled in a public school of another district within or out of the state, he or she may be admitted to school and placed in the grade of enrollment in the district of former attendance, at the discretion of the school administration of the district entered.