California's state disability insurance program (SDI) doesn't require that you be so disabled you can't work. The program is designed to make up for lost income due to a disability. If your disability allows you to work part-time -- but you're not earning what you used to -- the fact you're working doesn't disqualify you.
To qualify for SDI, your injury or illness must keep you out of work at least eight consecutive days. You must be under the care of a qualified medical professional or a religious practitioner -- a Christian Science healer, say -- who is registered with and approved by the state. Even if you were unemployed when the disability hit, you can qualify for SDI if your condition prevents you from looking for work. The state details its other requirements online.
Benefits and Wages
Your disability insurance bases your maximum benefit on your past earnings. If you lose some or all of your income due to your condition, the program will make up the lost wages, up to the limit of your maximum benefit. Working part-time could reduce your benefits by the amount you are being paid. For example, suppose your maximum benefit is $750 per pay period. If your part-time work pays $350 per pay period, you'll only receive $400 from SDI.