What is the minimum amount a class-action settlement needs to be reported as income in California?

It depends on whether or not you are required to file a tax return or not.   If you are required to file a return, you have to include all of your income including certain settlements.  Class-action settlement proceeds are treated as proceeds from any other lawsuit. The IRS treats settlements for physical injury or sickness as non-taxable as long as the claimant did not receive a tax benefit by deducting the related medical expenses on previous years' tax returns. Physical conditions like insomnia or stomachaches may not be serious enough to qualify as "physical injury." Settlements for emotional distress arising from physical injury are also non-taxable. Settlements for emotional distress not caused by a physical injury are taxable, but the amount reported could be reduced by medical bills that were not deducted on previous tax returns.

See this chart to see if you are required to file a federal tax return.   For the state of California: 

Generally, you must file an income tax return if you’re a resident, part-year resident, or nonresident and:

• Are required to file a federal return
• Receive income from a source in California
• Have income above a certain amount

Should you file?  If you do not owe taxes or have to file, you may be able to get a refund.

• If you qualify for the California Earned Income Tax Credit (EITC), you can get up to $3,027
• If you had money withheld out of your paycheck for state taxes, you may be able to get a refund