Legal Question in Real Estate Law in California

That would depend on whose counter it is. If it was the buyer's counter to a seller's counter, no. If it was the seller's counter to the buyer's offer, or a buyer's counter, then of course the seller must sign it. The party withdrawing any offer, whether an original or any level of counter, must sign it. The other party's signature is only acknowledgment of receipt of the withdrawal and assent to it. Neither acknowledgment nor assent is required, however, for a withdrawal to be effective. Only delivery. If the properly executed withdrawal is delivered to the other party before acceptance of the offer or counter-offer, the withdrawal is legally binding with nothing more.