question for all the single moms out there

So since vday my baby daddy has not been around. He has been acting liking childish and stuff like that. I have a lawyer and stuff. I'm not putting his name on the birth certificate and baby will have my last name.   So my question is should I go after him for child support? The reason why I'm asking is because he has not bugged me or anything for a bit now and if I pick at him that there is things he may do that I don't want to happen. Like kidnapping baby or little things like that.