California's capital city of SACRAMENTO California would be the first state to require gun owners to buy liability insurance if the measure is approved.
People are killed by guns more than cars. Nancy Skinner said in a statement that gun owners don't have to carry liability insurance.
She said gun owners should shoulder some of the costs of gun violence.
There have been a number of recent mass shootings and a rise in gun violence in New York.
The first such insurance requirement in the United States was approved by the city of San Jose in January.
Sam Paredes is the executive director of Gun Owners of California.
He said the requirements are not in line with the constitution.
Paredes said that they don't believe you can put pre-emptive steps on the exercising of a constitutional right. It doesn't make sense to require someone to get insurance in order to keep their guns.
Skinner wants gun owners to be held civilly liable if their firearms are used to cause property damage, injury or death.
The bill would require gun owners to have insurance to cover losses from negligent or accidental use of their firearms. If they are stopped for something, they would have to show the police proof of insurance for their gun.
Another bill that would affect gun owners' costs was also objected to by Paredes.
The bill would impose an excise tax equal to 10% of the sales price of a handgun and 9% of the sales price of a long gun.
The bill would bring in more than $118 million a year for gun violence prevention.
Levine's bill would have to be approved by a two-thirds majority in the Legislature. Last year, his measure fell four votes short of the required number in the Assembly.
One of the firearms measures being considered by California lawmakers this year is a proposal that would make it easier to file lawsuits against gun-makers.