Trump is the pick of 39% likely Republican voters, while Cruz has the support of 32%, according to a poll
from the Field Research Corporation in California. John Kasich is in third place at 18%, while 11% are undecided.
Cracks in GOP rank-and-file also are reflected in the poll, as nearly 4 in 10 California Republicans (38%) say they would be "dissatisfied" or "upset" if Trump became their party's nominee, and nearly as many (34%) say this about Cruz.
The poll also notes wide differences among Republican voters across key regions of the state. Trump is holding the lead among likely Republican voters in two regions: the nine-county San Francisco Bay area and Southern California outside of Los Angeles County. While Cruz is leading in Los Angeles County and those living in the state's vast but sparsely populated interior, support for Kasich is evenly spread across the state, although he is stronger in the San Francisco Bay area.
This could be significant as the regional differences in preferences could split the state's allocation of its 172 delegates in the GOP convention.
In case of a contested convention, 52% Republicans say the party should award the nomination to Trump, while 48% say someone else should be nominated. In order to clinch the nomination before the convention, a majority of 1,237 delegates is required.
In a general election scenario, Hillary Clinton is leading Trump with 28-point advantage and a 23-point lead over Cruz among the overall California electorate.
The poll also reveals a significant "gender gap" in GOP voter preferences, as Trump leads Cruz among men by 17 percentage points and women have a preference for Cruz by 4 percentage points. By age, Cruz leading Trump by 9 points among GOP voters under age 50, and Trump is ahead among seniors aged 65 or older.
GOP voters with no high school education have a preference for Trump over Cruz, while post-graduates are dividing their preferences among all candidates.
While GOP voters view both Trump and Cruz positively, both are seen highly unfavorably among the state's overall electorate, according to the poll. Three in four voters statewide (74%) hold an unfavorable view of Trump, while 22% have a positive look. Sixty-four percent rate Cruz negatively, while 25% view him positively.
The poll was conducted March 24- April 4 among 1,400 registered voters in California, including 558 likely GOP voters for the state's June primary contest. The margin of error among the overall registered voter sample is plus-or-minus 3.2 percentage points, and for the Republicans, the margin of error is 4 percentage points.