Yes. Paternity Leave in California, is also considered Paid Family Leave. The most recent available Form 540 Booklet, page 43, excludes the Paid Family Leave from the State of California. Enter Form W-2 in the Wages & Income interview in the Federal section.
To enter Paid Family Leave specifically, do a search for 1099-G and use the Jump to link in the search results or scroll down in the Wages & Income section to Unemployment. Click Show More and Start. Enter Form 1099-G.
See this article for more details: Where do I report a 1099-G for unemployment or paid family leave?
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