If you turn it down, you very well may be determined ineligible for continuing benefits and would have to re-qualify with a new claim after this 3-month period is over.
States treat temporary periods of work within a claim year differently. In my state, the claim remains open, just inactive, and you can either choose to not make a continuing claim for a particular week by giving the reason or make a partial claim by reporting the wages earned in that week. I don't know about California.

