Those voters include independents who say they’ll vote in the Democratic primary.
The PPIC results are in stark contrast to a SurveyUSA poll out this week that showed Clinton with an 18-point lead over Sanders.
But the SurveyUSA poll relies on a majority of respondents with landlines (62 percent were interviewed by landline through automation; 38 percent were shown a questionnaire on their smart phone, tablet or other electronic device). Many veteran California pollsters and political analysts question whether that mix of respondents is representative of the state's electorate.
SurveyUSA is a national polling firm with less experience polling California than PPIC. The PPIC poll, in contrast, interviewed half of respondents on cell phones.
In addition, the new PPIC poll shows Sanders catching up to Clinton compared to its previous poll. Clinton led Sanders 48 percent to 41 percent in March.
As in other states, Clinton draws stronger support among registered Democrats (49 percent to 41 percent), older voters (59 percent of likely voters aged 45 and up to Sanders's 28 percent) and women (49 percent to 42 percent). Sanders fares better with younger voters (66 percent of those aged 18-to-44), men (46 percent to 42 percent) and likely voters who describe themselves as "very liberal" (64 percent to 35 percent).
Clinton leads Sanders among Latinos, 53 percent to 42 percent.
In potential November matchups, presumptive Republican nominee Donald Trump trails both Clinton and Sanders. Clinton has support from 49 percent of likely voters, while 39 percent favor Trump. In a matchup between Sanders and Trump, 53 percent of likely voters favor Sanders, 36 percent support Trump.
In California's open U.S. Senate race to replace retiring Democratic Sen. Barbara Boxer, Attorney General Kamala Harris continues to lead all other candidates. Her 27 percent support among likely voters tops Orange County Rep. Loretta Sanchez's 19 percent.
The two Democrats lead three Republicans: Former California Republican Party chairman Tom Del Beccaro polls 8 percent, businessman Ron Unz has 6 percent and another former state GOP chairman, Duf Sundheim, draws 3 percent.
That's significant because the top two finishers in California's June 7th election will advance to the November runoff under the state's open primary system.
Those results are similar to the March PPIC poll.
But nearly a third of likely voters remain undecided - including nearly half of all Republicans.
Prospective November Ballot Measures
Backers of three potential November ballot initiatives appear to be starting their campaigns in good shape.
A proposal to legalize recreational marijuana in California draws support from 60 percent of likely voters.
A ballot measure that would extend the Proposition 30 income tax increases on the wealthiest Californians that voters approved in 2012 has 58 percent support.
And two-thirds of likely voters say they'd vote for a cigarette tax increase.