"The lack of safety or comfort with disclosure raises concerns about the degree to which individuals are able to obtain sufficient support in school or in the workplace, as well as from those with whom they may be closest,” the study said.

Still, just 20 percent of respondents said they might delay treatment for fear of others finding out about a mental health problem. And 88 percent had sought treatment at some point.

In addition, about 70 percent of those surveyed said that they are satisfied with life.

The survey was administered in English and Spanish.

The study said that previous findings have shown “a large majority of individuals with mental health problems eventually obtain treatment but with significant delays to first contact.” It said delaying treatment is a pervasive problem in the country as a whole, where those suffering can wait years or even decades to get help.

RAND completed the study as part of an evaluation of the California Mental Health Services Authority's prevention and early intervention programs, designed to improve mental health outcomes.

CalMHSA Executive Director Wayne Clark says the group is making some headway into changing attitudes about mental health, with a broad-based statewide campaign. But with one Californian taking his or her own life nearly every two hours, Clark says making mental illness as easy to discuss as a broken arm will still be a project for the long haul.

"It's going to take that kind of longer-term investment to change how people deal with emotional issues in their families, how they deal with them in their neighborhoods and in their schools and in their workplace," he said.

Sara Hossaini contributed to this report.