Generally speaking, short-term disability payments aren't considered taxable income. Yet there are a few circumstances where disability actually can be taxable, such as when you are already receiving Unemployment Insurance (which is taxable income), you then get injured while on unemployment, and the resulting disability payments which supplant the unemployment benefits are then considered taxable. But, if that were to occur, you'd know that because you would get a tax Form 1099-G from your state government.
So, your answer is most likely no; you don't need to report your EDD disability payments on your federal or state tax return.
A more detailed answer to your question, particularly as it pertains to California EDD disability payments, is provided at the following link. You are respectfully invited to read that post for additional information:
Thank you for asking this important question.