Sixteen percent said such laws should be less strict, and 19% said they should remain the same, according to the Public Policy Institute of California Statewide Survey.
Participants were also asked: "How concerned about the threat of a mass shooting?" The responses varied:
The poll was released after officials say an employee killed nine people Wednesday at a VTA railyard in San Jose and then killed himself as law enforcement rushed in.
San Jose mass shooting: Light rail operator, father of 2, was killed while helping co-workers hide
It was the 15th mass killing in the nation this year, all of them shootings that have claimed at least four lives each for a total of 87 deaths, according to a database compiled by The Associated Press, USA Today and Northeastern University.
Meanwhile, Texas is poised to remove one of its last major gun restrictions after lawmakers approved allowing people to carry handguns without a license, and the background check and training that go with it.
The Republican-dominated Legislature approved the measure Monday, sending it to Gov. Greg Abbott, who has said he will sign it despite the objections of law enforcement groups who say it would endanger the public and police.
The Associated Press contributed to this report.