Legally, your not obligated to give her shit, if you have doubts as to that being your child in the first place. You actually don't have any obligation unless (1) You accept that it is your child or (2) You take a paternity test and turns out to be yours.
So basically you have up until the time u take the test to not give her shit. But that bad part about that is, once she has the proof that it is yours, she can really fucc ya with the child support.
Basically she can fucc ya more ways then one, if she really wanted to. If I was u, I would try to stay on semi good terms with her. Cuz all she got to do is call down, say u haven't been giving child support, and they will take money straight from your muthafuccin checks without checkin to see if you have been payin or not. They did that to my cuz, without even checkin first if he payed or not. They act first and the rarely ask questions later. Unless of course u ain't got no job. Then they can't do shit.