As soon as a man utters or signs a paper for a civil divorce, then it counts as a Shar'i divorce because the Shari'a does not distinguish between words of divorce to the state or otherwise. Any utterance of divorce is divorce. So if he had uttered any statement or signed anything regarding civil divorce, then the 'idda waiting period would begin on that day.* Ignorance of the matter does not change anything either.
*Divorce can only occur during a wife's time of purity (i.e. not on menstruation) in which they have not co-habited. If those conditions were not met, it counts as one divorce but it does not apply and they are still married. If he still wants to divorce her then he waits until those two conditions are met and utters words of divorce again. If he continues forth with the civil divorce proceedings in any way that would indicate by words or signatures that he is divorcing her, then that applies as well.
The reason for the above two conditions is that Allah wants to put hurdles in front of divorce so that it does not happen easily.
Lastly, divorce occurs through any means or words in which the intention was clearly for the sake of divorce. It can be in any language and it can be by the written word as well. If he is asked, are you divorcing your wife, and he says "yes," then it applies.
Misconception: that for a divorce to occur, he has to repeat it three times. This is not the case. Once is sufficient. To repeat it three times is a bid'a that was initiated to hurt women. Courts in the past used to consider it a three times divorce if a man did that. Thus, he could not take back his wife unless she had remarried, consummated, then divorced again.