I don't think so.  You didn't have to pay her child support for that year, and I hope that doesn't get used against you, if this woman takes you to court.

But I doubt that she will.  If her husband (now ex-husband) signed the birth certificate, and supported the child as his own, and especially if you signed anything giving up your parental rights, she's going absolutely nowhere with this.  I'm guessing she didn't get as much money as she wanted out of the divorce, here.  And I'd also assume that she's getting child support from her ex-husband, until I saw a divorce decree with her name on it that said otherwise.  She can't legally collect from both of you.