The lawsuit also cites environmental damage caused by the spewing methane, the prime component of natural gas and a far more potent greenhouse gas than carbon dioxide.
A spokeswoman said the company doesn't comment on pending litigation and was focused on stopping the leak, which it expects to plug by the end of the month.
SoCalGas said it paid $50 million through December to try to cap the leak and relocate people, but the number of families it has relocated since then has soared and work at the leaking well continues.
It is also facing potential class-action lawsuits from residents and businesses as well as suits from regional air regulators and city and county authorities.
The leak stems from an underground pipeline rupture at the company's 3,600-acre Aliso Canyon natural gas storage field. It marks the largest such leak ever in California and at its height accounted for a fourth of all methane emissions statewide.
The stench of odorized methane fumes has sickened scores of people and led to the temporary relocation of thousands of residents from the Porter Ranch community of northern Los Angeles at the edge of the crippled underground gas storage field.
The state lawsuit, filed in Los Angeles County Superior Court, seeks unspecified civil penalties, and court orders requiring the utility to immediately take all steps necessary to mitigate the leak.
Several attempts to halt the methane release have failed, and the company is drilling relief wells to intersect the crippled pipeline to plug the leak, an effort that could take several more weeks.
Also on Tuesday, the federal Pipeline and Hazardous Materials Safety Administration got involved for the first time Tuesday, saying it is working to propose new regulations for gas storage and directing operators to "inspect and take immediate actions to ensure the safety of underground natural gas storage facilities across the country."
U.S. Rep. Brad Sherman, a Democrat who lives in the Porter Ranch neighborhood that has been most affected by the gas leak, said the agency's advisory amounted to a note to industry saying, "not just please, but pretty please" follow the American Petroleum Institute's recommended practices for gas storage.
And California Sens. Barbara Boxer and Dianne Feinstein, both Democrats, introduced a legislative amendment passed Tuesday that would ask the U.S. Department of Energy to investigate and stop the Aliso Canyon leak and prevent similar disasters at the nation's more than 400 underground natural-gas storage sites.