SAN FRANCISCO  California officials will investigate accusations that the Mormon Church neglected to report a battery of nonmonetary contributions  including phone banks, a Web site and commercials  on behalf of a ballot measure to ban same-sex marriage.

Roman Porter, the executive director of the Fair Political Practices Commission, which oversees California campaign finance laws, signed off on the investigation after reviewing a sworn complaint filed on Nov. 13.

The complaint, filed by Fred Karger, founder of the group Californians Against Hate, asserted that the church’s reported contributions  about $5,000, according to state election filings  vastly underestimated its actual efforts in passing Proposition 8, which amended the state’s Constitution to recognize only male-female marriage.

Broadly speaking, California state law requires disclosure of any money spent or services provided to influence the outcome of an election.