In California, it is the ordination or investment by the denomination that gives each clergy member the authority to perform the marriage rite. Family Code, Sections 400-402 are the statutes pertaining to whom can solemnize a marriage in California.

CALIFORNIA CODES
FAMILY.CODE
SECTION 400-402


400. Marriage may be solemnized by any of the following who is of the age of 18 years or older:
(a) A priest, minister, or rabbi of any religious denomination.
(b) A judge or retired judge, commissioner of civil marriages or retired commissioner of civil marriages, commissioner or retired commissioner, or assistant commissioner of a court of record in this
state.
(c) A judge or magistrate who has resigned from office.
(d) Any of the following judges or magistrates of the United States:
(1) A justice or retired justice of the United States Supreme Court.
(2) A judge or retired judge of a court of appeals, a district court, or a court created by an act of Congress the judges of which are entitled to hold office during good behavior.
(3) A judge or retired judge of a bankruptcy court or a tax court.

(4) A United States magistrate or retired magistrate.
(e) A legislator or constitutional officer of this state or a member of Congress who represents a district within this state, while that person holds office.

The marriage officiant who performs the marriage ceremony must know the California laws regarding the performance of a marriage and the requirements for officiants. Family Code, Sections 420-425 are the statutes pertaining to the performance of a marriage in California.

CALIFORNIA CODES
FAMILY.CODE
SECTION 421-425

421. Before solemnizing a marriage, the person solemnizing the marriage shall require the presentation of the marriage license. If the person solemnizing the marriage has reason to doubt the correctness of the statement of facts in the marriage license, the person must be satisfied as to the correctness of the statement of facts before solemnizing the marriage. For this purpose, the person may administer oaths and examine the parties and witnesses in the same manner as the county clerk does before issuing the license.

422. The person solemnizing a marriage shall make, sign, and endorse upon or attach to the marriage license a statement, in the form prescribed by the State Department of Health Services, showing all of the following:
(a) The fact, date (month, day, year), and place (city and county) of solemnization.
(b) The names and places of residence of one or more witnesses to the ceremony.
(c) The official position of the person solemnizing the marriage, or of the denomination of which that person is a priest, minister,rabbi, or member of the clergy.
(d) The person solemnizing the marriage shall also type or print the person's name and address.

423. The person solemnizing the marriage shall return the marriage license, endorsed as required in Section 422, to the county recorder of the county in which the license was issued within 10 days after the ceremony.

424. At the request of, and for, either party to a marriage, the person solemnizing the marriage shall issue a marriage certificate showing the facts specified in Section 422.

425. If no record of the solemnization of a marriage previously contracted is known to exist, the parties may purchase a License and Certificate of Declaration of Marriage from the county clerk in the parties' county of residence. The license and certificate shall be returned to the county recorder of the county in which the license was issued. source